diff --git a/pkg/pod/status.go b/pkg/pod/status.go
index dbb87f420c8..7381b216df4 100644
--- a/pkg/pod/status.go
+++ b/pkg/pod/status.go
@@ -125,7 +125,7 @@ func MakeTaskRunStatus(ctx context.Context, logger *zap.SugaredLogger, tr v1.Tas
 
 	sortPodContainerStatuses(pod.Status.ContainerStatuses, pod.Spec.Containers)
 
-	complete := areContainersCompleted(ctx, pod) || pod.Status.Phase == corev1.PodSucceeded || DidTaskRunFail(pod)
+	complete := areContainersCompleted(ctx, pod) || isPodCompleted(pod)
 
 	if complete {
 		onError, ok := tr.Annotations[v1.PipelineTaskOnErrorAnnotation]
@@ -636,6 +636,30 @@ func updateIncompleteTaskRunStatus(trs *v1.TaskRunStatus, pod *corev1.Pod) {
 	}
 }
 
+// isPodCompleted checks if the given pod is completed.
+// A pod is considered completed if its phase is either "Succeeded" or "Failed".
+//
+// If it is foreseeable that the pod will eventually be in a failed state,
+// but it remains in a Running status for a visible period of time, it should be considered completed in advance.
+//
+// For example, when certain steps encounter OOM, only the pods that have timed out will change to a failed state,
+// we should consider them completed in advance.
+func isPodCompleted(pod *corev1.Pod) bool {
+	if pod.Status.Phase == corev1.PodSucceeded || pod.Status.Phase == corev1.PodFailed {
+		return true
+	}
+	for _, s := range pod.Status.ContainerStatuses {
+		if IsContainerStep(s.Name) {
+			if s.State.Terminated != nil {
+				if isOOMKilled(s) {
+					return true
+				}
+			}
+		}
+	}
+	return false
+}
+
 // DidTaskRunFail check the status of pod to decide if related taskrun is failed
 func DidTaskRunFail(pod *corev1.Pod) bool {
 	if pod.Status.Phase == corev1.PodFailed {
diff --git a/pkg/pod/status_test.go b/pkg/pod/status_test.go
index a963cf6aa92..eb5a4695a33 100644
--- a/pkg/pod/status_test.go
+++ b/pkg/pod/status_test.go
@@ -847,7 +847,7 @@ func TestMakeTaskRunStatus(t *testing.T) {
 			}},
 		},
 		want: v1.TaskRunStatus{
-			Status: statusFailure(v1.TaskRunReasonFailed.String(), "\"step-state-name\" exited with code 123"),
+			Status: statusRunning(),
 			TaskRunStatusFields: v1.TaskRunStatusFields{
 				Steps: []v1.StepState{{
 					ContainerState: corev1.ContainerState{
@@ -859,9 +859,7 @@ func TestMakeTaskRunStatus(t *testing.T) {
 					Container: "step-state-name",
 				}},
 				Sidecars:  []v1.SidecarState{},
-				Artifacts: &v1.Artifacts{},
-				// We don't actually care about the time, just that it's not nil
-				CompletionTime: &metav1.Time{Time: time.Now()},
+				Artifacts: nil,
 			},
 		},
 	}, {
@@ -885,7 +883,7 @@ func TestMakeTaskRunStatus(t *testing.T) {
 			}},
 		},
 		want: v1.TaskRunStatus{
-			Status: statusFailure(v1.TaskRunReasonFailed.String(), "\"step-state-name\" exited with code 123"),
+			Status: statusRunning(),
 			TaskRunStatusFields: v1.TaskRunStatusFields{
 				Steps: []v1.StepState{{
 					ContainerState: corev1.ContainerState{
@@ -898,9 +896,7 @@ func TestMakeTaskRunStatus(t *testing.T) {
 					ImageID:   "image-id",
 				}},
 				Sidecars:  []v1.SidecarState{},
-				Artifacts: &v1.Artifacts{},
-				// We don't actually care about the time, just that it's not nil
-				CompletionTime: &metav1.Time{Time: time.Now()},
+				Artifacts: nil,
 			},
 		},
 	}, {
@@ -1454,6 +1450,46 @@ func TestMakeTaskRunStatus(t *testing.T) {
 				CompletionTime: &metav1.Time{Time: time.Now()},
 			},
 		},
+	}, {
+		desc: "oom occurred in the pod",
+		podStatus: corev1.PodStatus{
+			Phase: corev1.PodRunning,
+			ContainerStatuses: []corev1.ContainerStatus{{
+				Name: "step-one",
+				State: corev1.ContainerState{
+					Terminated: &corev1.ContainerStateTerminated{
+						Reason:   oomKilled,
+						ExitCode: 137,
+					},
+				},
+			}, {
+				Name:  "step-two",
+				State: corev1.ContainerState{},
+			}},
+		},
+		want: v1.TaskRunStatus{
+			Status: statusFailure(v1.TaskRunReasonFailed.String(), "\"step-one\" exited with code 137"),
+			TaskRunStatusFields: v1.TaskRunStatusFields{
+				Steps: []v1.StepState{{
+					ContainerState: corev1.ContainerState{
+						Terminated: &corev1.ContainerStateTerminated{
+							Reason:   oomKilled,
+							ExitCode: 137,
+						},
+					},
+					Name:      "one",
+					Container: "step-one",
+				}, {
+					ContainerState: corev1.ContainerState{},
+					Name:           "two",
+					Container:      "step-two",
+				}},
+				Sidecars:  []v1.SidecarState{},
+				Artifacts: &v1.Artifacts{},
+				// We don't actually care about the time, just that it's not nil
+				CompletionTime: &metav1.Time{Time: time.Now()},
+			},
+		},
 	}, {
 		desc: "the failed task show task results",
 		podStatus: corev1.PodStatus{