diff --git a/pkg/controller.v1/common/job.go b/pkg/controller.v1/common/job.go
index 825afdf8b1..d8a494dd0c 100644
--- a/pkg/controller.v1/common/job.go
+++ b/pkg/controller.v1/common/job.go
@@ -421,7 +421,7 @@ func (jc *JobController) CleanupJob(runPolicy *apiv1.RunPolicy, jobStatus apiv1.
 	currentTime := time.Now()
 	metaObject, _ := job.(metav1.Object)
 	ttl := runPolicy.TTLSecondsAfterFinished
-	if ttl == nil {
+	if ttl == nil || trainutil.IsJobSuspended(runPolicy) {
 		return nil
 	}
 	duration := time.Second * time.Duration(*ttl)
diff --git a/pkg/controller.v1/tensorflow/job_test.go b/pkg/controller.v1/tensorflow/job_test.go
index c7e5a43c45..df146ef15a 100644
--- a/pkg/controller.v1/tensorflow/job_test.go
+++ b/pkg/controller.v1/tensorflow/job_test.go
@@ -663,6 +663,30 @@ 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),
+			runPolicy: &kubeflowv1.RunPolicy{
+				TTLSecondsAfterFinished: nil,
+				Suspend:                 ptr.To(true),
+			},
+			jobStatus: kubeflowv1.JobStatus{
+				CompletionTime: nil,
+			},
+			wantTFJobIsRemoved: false,
+			wantErr:            false,
+		}),
+		Entry("No error with TTL is set and completionTime is nil, if suspended", &cleanUpCases{
+			tfJob: tftestutil.NewTFJobWithCleanupJobDelay(1, 2, 0, ptr.To[int32](10)),
+			runPolicy: &kubeflowv1.RunPolicy{
+				TTLSecondsAfterFinished: ptr.To[int32](10),
+				Suspend:                 ptr.To(true),
+			},
+			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)),
 			runPolicy: &kubeflowv1.RunPolicy{