diff --git a/Makefile b/Makefile
index ccb5b354..eb201253 100644
--- a/Makefile
+++ b/Makefile
@@ -56,8 +56,7 @@ test-client:
 .PHONY: test-client
 
 test-integration: openapi-spec
-	@echo "skip integration tests now, ref https://github.com/kubernetes/kubernetes/issues/119220"
-	# hack/make-rules/test-integration.sh $(WHAT)
+	hack/make-rules/test-integration.sh $(WHAT)
 .PHONY: test-integration
 
 e2e:
diff --git a/pkg/controller/statefulset/stateful_set_control.go b/pkg/controller/statefulset/stateful_set_control.go
index bc744596..68b1b480 100644
--- a/pkg/controller/statefulset/stateful_set_control.go
+++ b/pkg/controller/statefulset/stateful_set_control.go
@@ -416,13 +416,27 @@ func (ssc *defaultStatefulSetControl) updateStatefulSet(
 		if replicas[i] == nil {
 			continue
 		}
-		// delete and recreate failed pods
-		if isFailed(replicas[i]) {
-			ssc.recorder.Eventf(set, v1.EventTypeWarning, "RecreatingFailedPod",
-				"StatefulSet %s/%s is recreating failed Pod %s",
-				set.Namespace,
-				set.Name,
-				replicas[i].Name)
+		// Delete and recreate pods which finished running.
+		//
+		// Note that pods with phase Succeeded will also trigger this event. This is
+		// because final pod phase of evicted or otherwise forcibly stopped pods
+		// (e.g. terminated on node reboot) is determined by the exit code of the
+		// container, not by the reason for pod termination. We should restart the pod
+		// regardless of the exit code.
+		if isFailed(replicas[i]) || isSucceeded(replicas[i]) {
+			if isFailed(replicas[i]) {
+				ssc.recorder.Eventf(set, v1.EventTypeWarning, "RecreatingFailedPod",
+					"StatefulSet %s/%s is recreating failed Pod %s",
+					set.Namespace,
+					set.Name,
+					replicas[i].Name)
+			} else {
+				ssc.recorder.Eventf(set, v1.EventTypeNormal, "RecreatingTerminatedPod",
+					"StatefulSet %s/%s is recreating terminated Pod %s",
+					set.Namespace,
+					set.Name,
+					replicas[i].Name)
+			}
 			if err := ssc.podControl.DeleteStatefulPod(set, replicas[i]); err != nil {
 				return &status, err
 			}
diff --git a/pkg/controller/statefulset/stateful_set_control_test.go b/pkg/controller/statefulset/stateful_set_control_test.go
index 154b33de..0c659937 100644
--- a/pkg/controller/statefulset/stateful_set_control_test.go
+++ b/pkg/controller/statefulset/stateful_set_control_test.go
@@ -91,6 +91,7 @@ func TestStatefulSetControl(t *testing.T) {
 		{ScalesDown, simpleSetFn},
 		{ReplacesPods, largeSetFn},
 		{RecreatesFailedPod, simpleSetFn},
+		{RecreatesSucceededPod, simpleSetFn},
 		{CreatePodFailure, simpleSetFn},
 		{UpdatePodFailure, simpleSetFn},
 		{UpdateSetStatusFailure, simpleSetFn},
@@ -267,7 +268,7 @@ func ReplacesPods(t *testing.T, set *apps.StatefulSet, invariants invariantFunc)
 	}
 }
 
-func RecreatesFailedPod(t *testing.T, set *apps.StatefulSet, invariants invariantFunc) {
+func recreatesPod(t *testing.T, set *apps.StatefulSet, invariants invariantFunc, phase v1.PodPhase) {
 	client := fake.NewSimpleClientset()
 	pcClient := pcfake.NewSimpleClientset(set)
 	spc, _, ssc, stop := setupController(pcClient, client)
@@ -290,7 +291,7 @@ func RecreatesFailedPod(t *testing.T, set *apps.StatefulSet, invariants invarian
 	if err != nil {
 		t.Error(err)
 	}
-	pods[0].Status.Phase = v1.PodFailed
+	pods[0].Status.Phase = phase
 	spc.podsIndexer.Update(pods[0])
 	if err := ssc.UpdateStatefulSet(set, pods); err != nil {
 		t.Errorf("Error updating StatefulSet %s", err)
@@ -307,6 +308,14 @@ func RecreatesFailedPod(t *testing.T, set *apps.StatefulSet, invariants invarian
 	}
 }
 
+func RecreatesFailedPod(t *testing.T, set *apps.StatefulSet, invariants invariantFunc) {
+	recreatesPod(t, set, invariants, v1.PodFailed)
+}
+
+func RecreatesSucceededPod(t *testing.T, set *apps.StatefulSet, invariants invariantFunc) {
+	recreatesPod(t, set, invariants, v1.PodSucceeded)
+}
+
 func CreatePodFailure(t *testing.T, set *apps.StatefulSet, invariants invariantFunc) {
 	client := fake.NewSimpleClientset()
 	pcClient := pcfake.NewSimpleClientset(set)
diff --git a/pkg/controller/statefulset/stateful_set_utils.go b/pkg/controller/statefulset/stateful_set_utils.go
index e51b85fa..4398268b 100644
--- a/pkg/controller/statefulset/stateful_set_utils.go
+++ b/pkg/controller/statefulset/stateful_set_utils.go
@@ -214,6 +214,11 @@ func isFailed(pod *v1.Pod) bool {
 	return pod.Status.Phase == v1.PodFailed
 }
 
+// isSucceeded returns true if pod has a Phase of PodSucceeded
+func isSucceeded(pod *v1.Pod) bool {
+	return pod.Status.Phase == v1.PodSucceeded
+}
+
 // isTerminating returns true if pod's DeletionTimestamp has been set
 func isTerminating(pod *v1.Pod) bool {
 	return pod.DeletionTimestamp != nil
diff --git a/test/integration/statefulset/statefulset_test.go b/test/integration/statefulset/statefulset_test.go
index b439455f..61f0364c 100644
--- a/test/integration/statefulset/statefulset_test.go
+++ b/test/integration/statefulset/statefulset_test.go
@@ -25,6 +25,7 @@ import (
 	integrationutil "github.com/pingcap/advanced-statefulset/test/integration/util"
 	v1 "k8s.io/api/core/v1"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
+	"k8s.io/apimachinery/pkg/types"
 	"k8s.io/apimachinery/pkg/util/wait"
 )
 
@@ -79,17 +80,19 @@ func TestDeletingAndFailedPods(t *testing.T) {
 	stopCh := runControllerAndInformers(rm, informers, pcinformers)
 	defer close(stopCh)
 
+	podCount := 3
+
 	labelMap := labelMap()
-	sts := newSTS("sts", ns.Name, 2)
+	sts := newSTS("sts", ns.Name, podCount)
 	stss, _ := createSTSsPods(t, c, pcc, []*appsv1.StatefulSet{sts}, []*v1.Pod{})
 	sts = stss[0]
 	waitSTSStable(t, pcc, sts)
 
-	// Verify STS creates 2 pods
+	// Verify STS creates 3 pods
 	podClient := c.CoreV1().Pods(ns.Name)
 	pods := getPods(t, podClient, labelMap)
-	if len(pods.Items) != 2 {
-		t.Fatalf("len(pods) = %d, want 2", len(pods.Items))
+	if len(pods.Items) != podCount {
+		t.Fatalf("len(pods) = %d, want %d", len(pods.Items), podCount)
 	}
 
 	// Set first pod as deleting pod
@@ -108,23 +111,47 @@ func TestDeletingAndFailedPods(t *testing.T) {
 		pod.Status.Phase = v1.PodFailed
 	})
 
+	// Set third pod as succeeded pod
+	succeededPod := &pods.Items[2]
+	updatePodStatus(t, podClient, succeededPod.Name, func(pod *v1.Pod) {
+		pod.Status.Phase = v1.PodSucceeded
+	})
+
+	exists := func(pods []v1.Pod, uid types.UID) bool {
+		for _, pod := range pods {
+			if pod.UID == uid {
+				return true
+			}
+		}
+		return false
+	}
+
 	if err := wait.PollImmediate(pollInterval, pollTimeout, func() (bool, error) {
-		// Verify only 2 pods exist: deleting pod and new pod replacing failed pod
+		// Verify only 3 pods exist: deleting pod and new pod replacing failed pod
 		pods = getPods(t, podClient, labelMap)
-		if len(pods.Items) != 2 {
+		if len(pods.Items) != podCount {
 			return false, nil
 		}
 		// Verify deleting pod still exists
 		// Immediately return false with an error if it does not exist
-		if pods.Items[0].UID != deletingPod.UID && pods.Items[1].UID != deletingPod.UID {
+		if !exists(pods.Items, deletingPod.UID) {
 			return false, fmt.Errorf("expected deleting pod %s still exists, but it is not found", deletingPod.Name)
 		}
 		// Verify failed pod does not exist anymore
-		if pods.Items[0].UID == failedPod.UID || pods.Items[1].UID == failedPod.UID {
+		if exists(pods.Items, failedPod.UID) {
 			return false, nil
 		}
-		// Verify both pods have non-failed status
-		return pods.Items[0].Status.Phase != v1.PodFailed && pods.Items[1].Status.Phase != v1.PodFailed, nil
+		// Verify succeeded pod does not exist anymore
+		if exists(pods.Items, succeededPod.UID) {
+			return false, nil
+		}
+		// Verify all pods have non-terminated status
+		for _, pod := range pods.Items {
+			if pod.Status.Phase == v1.PodFailed || pod.Status.Phase == v1.PodSucceeded {
+				return false, nil
+			}
+		}
+		return true, nil
 	}); err != nil {
 		t.Fatalf("failed to verify failed pod %s has been replaced with a new non-failed pod, and deleting pod %s survives: %v", failedPod.Name, deletingPod.Name, err)
 	}
@@ -135,13 +162,13 @@ func TestDeletingAndFailedPods(t *testing.T) {
 	})
 
 	if err := wait.PollImmediate(pollInterval, pollTimeout, func() (bool, error) {
-		// Verify only 2 pods exist: new non-deleting pod replacing deleting pod and the non-failed pod
+		// Verify only 3 pods exist: new non-deleting pod replacing deleting pod and the non-failed pod
 		pods = getPods(t, podClient, labelMap)
-		if len(pods.Items) != 2 {
+		if len(pods.Items) != podCount {
 			return false, nil
 		}
 		// Verify deleting pod does not exist anymore
-		return pods.Items[0].UID != deletingPod.UID && pods.Items[1].UID != deletingPod.UID, nil
+		return !exists(pods.Items, deletingPod.UID), nil
 	}); err != nil {
 		t.Fatalf("failed to verify deleting pod %s has been replaced with a new non-deleting pod: %v", deletingPod.Name, err)
 	}