diff --git a/airflow/www/static/js/task-instances.js b/airflow/www/static/js/task-instances.js
index 39b36badbe548f..a106c00d4912a8 100644
--- a/airflow/www/static/js/task-instances.js
+++ b/airflow/www/static/js/task-instances.js
@@ -20,12 +20,18 @@
 /* global window, dagTZ, moment, convertSecsToHumanReadable */
 
 // We don't re-import moment again, otherwise webpack will include it twice in the bundle!
-import { defaultFormat, formatDateTime } from './datetime-utils';
 import { escapeHtml } from './base';
+import { defaultFormat, formatDateTime } from './datetime-utils';
 
 function makeDateTimeHTML(start, end) {
+  // check task ended or not
+  if (end && end instanceof moment) {
+    return (
+      `Started: ${start.format(defaultFormat)} <br> Ended: ${end.format(defaultFormat)} <br>`
+    )
+  }
   return (
-    `Started: ${start.format(defaultFormat)} <br> Ended: ${end.format(defaultFormat)} <br>`
+    `Started: ${start.format(defaultFormat)} <br> Ended: Not ended yet <br>`
   )
 }
 
@@ -47,13 +53,15 @@ function generateTooltipDateTimes(startDate, endDate, dagTZ) {
   // Generate User's Local Start and End Date
   startDate.tz(localTZ);
   tooltipHTML += `<br><strong>Local: ${startDate.format(tzFormat)}</strong><br>`;
-  tooltipHTML += makeDateTimeHTML(startDate, endDate.tz(localTZ));
+  const localEndDate = endDate && endDate instanceof moment ? endDate.tz(localTZ) : endDate;
+  tooltipHTML += makeDateTimeHTML(startDate, localEndDate);
 
   // Generate DAG's Start and End Date
   if (dagTZ !== 'UTC' && dagTZ !== localTZ) {
     startDate.tz(dagTZ);
     tooltipHTML += `<br><strong>DAG's TZ: ${startDate.format(tzFormat)}</strong><br>`;
-    tooltipHTML += makeDateTimeHTML(startDate, endDate.tz(dagTZ));
+    const dagTZEndDate = endDate && endDate instanceof moment ? endDate.tz(dagTZ) : endDate;
+    tooltipHTML += makeDateTimeHTML(startDate, dagTZEndDate);
   }
 
   return tooltipHTML;