diff --git a/core/src/main/scala/org/apache/spark/ui/jobs/AllJobsPage.scala b/core/src/main/scala/org/apache/spark/ui/jobs/AllJobsPage.scala
index 18be0870746e..7065f6a4df1a 100644
--- a/core/src/main/scala/org/apache/spark/ui/jobs/AllJobsPage.scala
+++ b/core/src/main/scala/org/apache/spark/ui/jobs/AllJobsPage.scala
@@ -629,7 +629,8 @@ private[ui] class JobPagedTable(
         {if (job.numSkippedStages > 0) s"(${job.numSkippedStages} skipped)"}
       </td>
       <td class="progress-cell">
-        {UIUtils.makeProgressBar(started = job.numActiveTasks, completed = job.numCompletedTasks,
+        {UIUtils.makeProgressBar(started = job.numActiveTasks,
+        completed = job.completedIndices.size,
         failed = job.numFailedTasks, skipped = job.numSkippedTasks,
         reasonToNumKilled = job.reasonToNumKilled, total = job.numTasks - job.numSkippedTasks)}
       </td>
diff --git a/core/src/main/scala/org/apache/spark/ui/jobs/JobProgressListener.scala b/core/src/main/scala/org/apache/spark/ui/jobs/JobProgressListener.scala
index 1cf03e1541d1..46c50d656f5d 100644
--- a/core/src/main/scala/org/apache/spark/ui/jobs/JobProgressListener.scala
+++ b/core/src/main/scala/org/apache/spark/ui/jobs/JobProgressListener.scala
@@ -423,6 +423,7 @@ class JobProgressListener(conf: SparkConf) extends SparkListener with Logging {
         jobData.numActiveTasks -= 1
         taskEnd.reason match {
           case Success =>
+            jobData.completedIndices.add((taskEnd.stageId, info.index))
             jobData.numCompletedTasks += 1
           case kill: TaskKilled =>
             jobData.reasonToNumKilled = jobData.reasonToNumKilled.updated(
diff --git a/core/src/main/scala/org/apache/spark/ui/jobs/UIData.scala b/core/src/main/scala/org/apache/spark/ui/jobs/UIData.scala
index ac1a74ad8029..fde21bc51f68 100644
--- a/core/src/main/scala/org/apache/spark/ui/jobs/UIData.scala
+++ b/core/src/main/scala/org/apache/spark/ui/jobs/UIData.scala
@@ -62,6 +62,7 @@ private[spark] object UIData {
     var numTasks: Int = 0,
     var numActiveTasks: Int = 0,
     var numCompletedTasks: Int = 0,
+    var completedIndices: OpenHashSet[(Int, Int)] = new OpenHashSet[(Int, Int)](),
     var numSkippedTasks: Int = 0,
     var numFailedTasks: Int = 0,
     var reasonToNumKilled: Map[String, Int] = Map.empty,
diff --git a/core/src/test/scala/org/apache/spark/ui/UISeleniumSuite.scala b/core/src/test/scala/org/apache/spark/ui/UISeleniumSuite.scala
index 422837303642..d75b0fa86956 100644
--- a/core/src/test/scala/org/apache/spark/ui/UISeleniumSuite.scala
+++ b/core/src/test/scala/org/apache/spark/ui/UISeleniumSuite.scala
@@ -285,12 +285,7 @@ class UISeleniumSuite extends SparkFunSuite with WebBrowser with Matchers with B
       eventually(timeout(5 seconds), interval(50 milliseconds)) {
         goToUi(sc, "/jobs")
         find(cssSelector(".stage-progress-cell")).get.text should be ("2/2 (1 failed)")
-        // Ideally, the following test would pass, but currently we overcount completed tasks
-        // if task recomputations occur:
-        // find(cssSelector(".progress-cell .progress")).get.text should be ("2/2 (1 failed)")
-        // Instead, we guarantee that the total number of tasks is always correct, while the number
-        // of completed tasks may be higher:
-        find(cssSelector(".progress-cell .progress")).get.text should be ("3/2 (1 failed)")
+        find(cssSelector(".progress-cell .progress")).get.text should be ("2/2 (1 failed)")
       }
       val jobJson = getJson(sc.ui.get, "jobs")
       (jobJson \ "numTasks").extract[Int]should be (2)