diff --git a/pkg/controller/job/job_controller_test.go b/pkg/controller/job/job_controller_test.go
index 4a4ac7bb7cf1..84311ebd077e 100644
--- a/pkg/controller/job/job_controller_test.go
+++ b/pkg/controller/job/job_controller_test.go
@@ -1422,7 +1422,7 @@ func TestTrackJobStatusAndRemoveFinalizers(t *testing.T) {
 			wantSucceededPodsMetric: 3,
 			wantFailedPodsMetric:    3,
 		},
-		"succeeding job": {
+		"succeeding job by JobSuccessPolicy": {
 			pods: []*v1.Pod{
 				buildPod().uid("a").phase(v1.PodSucceeded).trackingFinalizer().Pod,
 				buildPod().uid("b").phase(v1.PodFailed).trackingFinalizer().Pod,
@@ -3834,6 +3834,70 @@ func TestSyncJobWithJobSuccessPolicy(t *testing.T) {
 				},
 			},
 		},
+		// In the current mechanism, the job controller adds Complete condition to Job
+		// even if some running pods still remain.
+		// So, we need to revisit here before we graduate the JobSuccessPolicy to beta.
+		// TODO(#123775): A Job might finish with ready!=0
+		// REF: https://github.com/kubernetes/kubernetes/issues/123775
+		"job with successPolicy; job has SuccessCriteriaMet and Complete condition when job meets to successPolicy and some pods still are running": {
+			enableJobSuccessPolicy: true,
+			job: batch.Job{
+				TypeMeta:   validTypeMeta,
+				ObjectMeta: validObjectMeta,
+				Spec: batch.JobSpec{
+					Selector:             validSelector,
+					Template:             validTemplate,
+					CompletionMode:       completionModePtr(batch.IndexedCompletion),
+					Parallelism:          ptr.To[int32](3),
+					Completions:          ptr.To[int32](3),
+					BackoffLimit:         ptr.To[int32](math.MaxInt32),
+					BackoffLimitPerIndex: ptr.To[int32](3),
+					SuccessPolicy: &batch.SuccessPolicy{
+						Rules: []batch.SuccessPolicyRule{{
+							SucceededIndexes: ptr.To("0,1"),
+							SucceededCount:   ptr.To[int32](1),
+						}},
+					},
+				},
+				Status: batch.JobStatus{
+					Conditions: []batch.JobCondition{
+						{
+							Type:    batch.JobSuccessCriteriaMet,
+							Status:  v1.ConditionTrue,
+							Reason:  batch.JobReasonSuccessPolicy,
+							Message: "Matched rules at index 0",
+						},
+					},
+				},
+			},
+			pods: []v1.Pod{
+				*buildPod().uid("a1").index("0").phase(v1.PodFailed).trackingFinalizer().Pod,
+				*buildPod().uid("a2").index("1").phase(v1.PodRunning).trackingFinalizer().Pod,
+				*buildPod().uid("b").index("1").phase(v1.PodSucceeded).trackingFinalizer().Pod,
+				*buildPod().uid("c").index("2").phase(v1.PodRunning).trackingFinalizer().Pod,
+			},
+			wantStatus: batch.JobStatus{
+				Failed:                  1,
+				Succeeded:               1,
+				Terminating:             ptr.To[int32](0),
+				CompletedIndexes:        "1",
+				UncountedTerminatedPods: &batch.UncountedTerminatedPods{},
+				Conditions: []batch.JobCondition{
+					{
+						Type:    batch.JobSuccessCriteriaMet,
+						Status:  v1.ConditionTrue,
+						Reason:  batch.JobReasonSuccessPolicy,
+						Message: "Matched rules at index 0",
+					},
+					{
+						Type:    batch.JobComplete,
+						Status:  v1.ConditionTrue,
+						Reason:  batch.JobReasonSuccessPolicy,
+						Message: "Matched rules at index 0",
+					},
+				},
+			},
+		},
 		"job with successPolicy and podFailurePolicy; job has a failed condition when job meets to both successPolicy and podFailurePolicy": {
 			enableJobSuccessPolicy: true,
 			enableJobFailurePolicy: true,