diff --git a/pkg/controller.v1/common/job.go b/pkg/controller.v1/common/job.go
index 825afdf8b1..ad27b6e35a 100644
--- a/pkg/controller.v1/common/job.go
+++ b/pkg/controller.v1/common/job.go
@@ -421,8 +421,8 @@ func (jc *JobController) CleanupJob(runPolicy *apiv1.RunPolicy, jobStatus apiv1.
 	currentTime := time.Now()
 	metaObject, _ := job.(metav1.Object)
 	ttl := runPolicy.TTLSecondsAfterFinished
-	if ttl == nil {
-		return nil
+	if ttl == nil || commonutil.IsSuspended(jobStatus) { 
+		return nil 
 	}
 	duration := time.Second * time.Duration(*ttl)
 	if jobStatus.CompletionTime == nil {
diff --git a/pkg/controller.v1/tensorflow/job_test.go b/pkg/controller.v1/tensorflow/job_test.go
index c7e5a43c45..5237c9601a 100644
--- a/pkg/controller.v1/tensorflow/job_test.go
+++ b/pkg/controller.v1/tensorflow/job_test.go
@@ -531,12 +531,12 @@ var _ = Describe("TFJob controller", func() {
 			testCases := []testCase{
 				{
 					description: "succeeded job with TTL 3s",
-					tfJob:       tftestutil.NewTFJobWithCleanupJobDelay(0, 1, 0, ptr.To[int32](3)),
+					tfJob:       tftestutil.NewTFJobWithCleanupJobDelay(0, 1, 0, ptr.To[int32](3), ptr.To(false)),
 					phase:       corev1.PodSucceeded,
 				},
 				{
 					description: "failed job with TTL 3s",
-					tfJob:       tftestutil.NewTFJobWithCleanupJobDelay(0, 1, 0, ptr.To[int32](3)),
+					tfJob:       tftestutil.NewTFJobWithCleanupJobDelay(0, 1, 0, ptr.To[int32](3), ptr.To(false)),
 					phase:       corev1.PodFailed,
 				},
 			}
@@ -655,7 +655,7 @@ var _ = Describe("Test for controller.v1/common", func() {
 			}
 		},
 		Entry("TFJob shouldn't be removed since TTL is nil", &cleanUpCases{
-			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, nil),
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, nil, ptr.To(false)),
 			runPolicy: &kubeflowv1.RunPolicy{
 				TTLSecondsAfterFinished: nil,
 			},
@@ -663,8 +663,19 @@ var _ = Describe("Test for controller.v1/common", func() {
 			wantTFJobIsRemoved: false,
 			wantErr:            false,
 		}),
+		Entry("No error with completionTime is nil if suspended", &cleanUpCases{
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, nil, ptr.To(true)),
+			runPolicy: &kubeflowv1.RunPolicy{
+				TTLSecondsAfterFinished: nil,
+			},
+			jobStatus: kubeflowv1.JobStatus{
+				CompletionTime: nil,
+			},
+			wantTFJobIsRemoved: false,
+			wantErr:            false,
+		}),
 		Entry("Error is occurred since completionTime is nil", &cleanUpCases{
-			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](10)),
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](10), ptr.To(false)),
 			runPolicy: &kubeflowv1.RunPolicy{
 				TTLSecondsAfterFinished: ptr.To[int32](10),
 			},
@@ -675,7 +686,7 @@ var _ = Describe("Test for controller.v1/common", func() {
 			wantErr:            true,
 		}),
 		Entry("TFJob is removed since exceeded TTL (TTL is 180s)", &cleanUpCases{
-			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](180)),
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](180), ptr.To(false)),
 			runPolicy: &kubeflowv1.RunPolicy{
 				TTLSecondsAfterFinished: ptr.To[int32](180),
 			},
@@ -688,7 +699,7 @@ var _ = Describe("Test for controller.v1/common", func() {
 			wantErr:            false,
 		}),
 		Entry("TFJob is removed since (TTL is 0s)", &cleanUpCases{
-			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](0)),
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](0), ptr.To(false)),
 			runPolicy: &kubeflowv1.RunPolicy{
 				TTLSecondsAfterFinished: ptr.To[int32](0),
 			},
diff --git a/pkg/controller.v1/tensorflow/testutil/tfjob.go b/pkg/controller.v1/tensorflow/testutil/tfjob.go
index 25da80d8b8..deb4c22fe4 100644
--- a/pkg/controller.v1/tensorflow/testutil/tfjob.go
+++ b/pkg/controller.v1/tensorflow/testutil/tfjob.go
@@ -34,14 +34,16 @@ func NewTFJobWithCleanPolicy(chief, worker, ps int, policy kubeflowv1.CleanPodPo
 	return tfJob
 }
 
-func NewTFJobWithCleanupJobDelay(chief, worker, ps int, ttl *int32) *kubeflowv1.TFJob {
+func NewTFJobWithCleanupJobDelay(chief, worker, ps int, ttl *int32, suspended *bool) *kubeflowv1.TFJob {
 	if chief == 1 {
 		tfJob := NewTFJobWithChief(worker, ps)
+		tfJob.Spec.RunPolicy.Suspend = suspended
 		tfJob.Spec.RunPolicy.TTLSecondsAfterFinished = ttl
 		tfJob.Spec.RunPolicy.CleanPodPolicy = kubeflowv1.CleanPodPolicyPointer(kubeflowv1.CleanPodPolicyNone)
 		return tfJob
 	}
 	tfJob := NewTFJob(worker, ps)
+	tfJob.Spec.RunPolicy.Suspend = suspended
 	tfJob.Spec.RunPolicy.TTLSecondsAfterFinished = ttl
 	tfJob.Spec.RunPolicy.CleanPodPolicy = kubeflowv1.CleanPodPolicyPointer(kubeflowv1.CleanPodPolicyNone)
 	return tfJob