diff --git a/ray-operator/controllers/ray/raycluster_controller.go b/ray-operator/controllers/ray/raycluster_controller.go
index a8fe122699..b544f53187 100644
--- a/ray-operator/controllers/ray/raycluster_controller.go
+++ b/ray-operator/controllers/ray/raycluster_controller.go
@@ -267,29 +267,27 @@ func (r *RayClusterReconciler) rayClusterReconcile(ctx context.Context, request
 				redisCleanupJob := redisCleanupJobs.Items[0]
 				r.Log.Info("Redis cleanup Job status", "Job name", redisCleanupJob.Name,
 					"Active", redisCleanupJob.Status.Active, "Succeeded", redisCleanupJob.Status.Succeeded, "Failed", redisCleanupJob.Status.Failed)
-				if redisCleanupJob.Status.Succeeded > 0 {
-					r.Log.Info(fmt.Sprintf(
-						"The Redis cleanup Job %s has been completed. "+
-							"The storage namespace %s in Redis has been fully deleted.",
-						redisCleanupJob.Name, redisCleanupJob.Annotations[utils.RayExternalStorageNSAnnotationKey]))
-					// Remove the finalizer from the RayCluster CR.
+				if condition, finished := utils.IsJobFinished(&redisCleanupJob); finished {
 					controllerutil.RemoveFinalizer(instance, utils.GCSFaultToleranceRedisCleanupFinalizer)
 					if err := r.Update(ctx, instance); err != nil {
-						r.Log.Error(err, "Failed to remove finalizer for RayCluster")
 						return ctrl.Result{RequeueAfter: DefaultRequeueDuration}, err
 					}
-					r.Log.Info(fmt.Sprintf(
-						"The Redis cleanup finalizer has been successfully removed from the RayCluster CR %s. "+
-							"We do not need to requeue the RayCluster CR anymore.", instance.Name))
+					switch condition {
+					case batchv1.JobComplete:
+						r.Log.Info(fmt.Sprintf(
+							"The Redis cleanup Job %s has been completed. "+
+								"The storage namespace %s in Redis has been fully deleted.",
+							redisCleanupJob.Name, redisCleanupJob.Annotations[utils.RayExternalStorageNSAnnotationKey]))
+					case batchv1.JobFailed:
+						r.Log.Info(fmt.Sprintf(
+							"The Redis cleanup Job %s has failed, requeue the RayCluster CR after 5 minute. "+
+								"You should manually delete the storage namespace %s in Redis and remove the RayCluster's finalizer. "+
+								"Please check https://docs.ray.io/en/master/cluster/kubernetes/user-guides/kuberay-gcs-ft.html for more details.",
+							redisCleanupJob.Name, redisCleanupJob.Annotations[utils.RayExternalStorageNSAnnotationKey]))
+					}
 					return ctrl.Result{}, nil
-				}
-				if redisCleanupJob.Status.Failed > 0 {
-					r.Log.Info(fmt.Sprintf(
-						"The Redis cleanup Job %s has failed, requeue the RayCluster CR after 5 minute. "+
-							"You should manually delete the storage namespace %s in Redis and remove the RayCluster's finalizer. "+
-							"Please check https://docs.ray.io/en/master/cluster/kubernetes/user-guides/kuberay-gcs-ft.html for more details.",
-						redisCleanupJob.Name, redisCleanupJob.Annotations[utils.RayExternalStorageNSAnnotationKey]))
-					return ctrl.Result{RequeueAfter: 5 * time.Minute}, nil
+				} else { // the redisCleanupJob is still running
+					return ctrl.Result{RequeueAfter: DefaultRequeueDuration}, nil
 				}
 			} else {
 				redisCleanupJob := r.buildRedisCleanupJob(*instance)
@@ -1169,6 +1167,8 @@ func (r *RayClusterReconciler) buildRedisCleanupJob(instance rayv1.RayCluster) b
 				ObjectMeta: pod.ObjectMeta,
 				Spec:       pod.Spec,
 			},
+			// make this job be best-effort only for 5 minutes.
+			ActiveDeadlineSeconds: pointer.Int64(300),
 		},
 	}
 
diff --git a/ray-operator/controllers/ray/raycluster_controller_fake_test.go b/ray-operator/controllers/ray/raycluster_controller_fake_test.go
index 511305f198..0e40fb9b0d 100644
--- a/ray-operator/controllers/ray/raycluster_controller_fake_test.go
+++ b/ray-operator/controllers/ray/raycluster_controller_fake_test.go
@@ -2231,10 +2231,12 @@ func Test_RedisCleanup(t *testing.T) {
 				assert.Nil(t, err, "Fail to get RayCluster list")
 				assert.Equal(t, 1, len(rayClusterList.Items))
 				assert.True(t, controllerutil.ContainsFinalizer(&rayClusterList.Items[0], utils.GCSFaultToleranceRedisCleanupFinalizer))
+				assert.Equal(t, int64(300), *jobList.Items[0].Spec.ActiveDeadlineSeconds)
 
 				// Simulate the Job succeeded.
 				job := jobList.Items[0]
 				job.Status.Succeeded = 1
+				job.Status.Conditions = []batchv1.JobCondition{{Type: batchv1.JobComplete, Status: corev1.ConditionTrue}}
 				err = fakeClient.Status().Update(ctx, &job)
 				assert.Nil(t, err, "Fail to update Job status")
 
diff --git a/ray-operator/controllers/ray/utils/util.go b/ray-operator/controllers/ray/utils/util.go
index 3927197493..1f765c92ad 100644
--- a/ray-operator/controllers/ray/utils/util.go
+++ b/ray-operator/controllers/ray/utils/util.go
@@ -12,6 +12,7 @@ import (
 	"time"
 	"unicode"
 
+	batchv1 "k8s.io/api/batch/v1"
 	"k8s.io/apimachinery/pkg/util/json"
 
 	"k8s.io/apimachinery/pkg/util/rand"
@@ -510,3 +511,15 @@ func FindContainerPort(container *corev1.Container, portName string, defaultPort
 	}
 	return defaultPort
 }
+
+// IsJobFinished checks whether the given Job has finished execution.
+// It does not discriminate between successful and failed terminations.
+// src: https://github.com/kubernetes/kubernetes/blob/a8a1abc25cad87333840cd7d54be2efaf31a3177/pkg/controller/job/utils.go#L26
+func IsJobFinished(j *batchv1.Job) (batchv1.JobConditionType, bool) {
+	for _, c := range j.Status.Conditions {
+		if (c.Type == batchv1.JobComplete || c.Type == batchv1.JobFailed) && c.Status == corev1.ConditionTrue {
+			return c.Type, true
+		}
+	}
+	return "", false
+}