diff --git a/karma.conf.js b/karma.conf.js
index e8875931c3..910821e602 100644
--- a/karma.conf.js
+++ b/karma.conf.js
@@ -235,6 +235,7 @@ module.exports = (config) => {
       {pattern: 'test/test/assets/*', included: false},
       {pattern: 'test/test/assets/dash-multi-codec/*', included: false},
       {pattern: 'test/test/assets/3675/*', included: false},
+      {pattern: 'test/test/assets/6339/*', included: false},
       {pattern: 'test/test/assets/dash-aes-128/*', included: false},
       {pattern: 'test/test/assets/hls-aes-256/*', included: false},
       {pattern: 'test/test/assets/hls-raw-aac/*', included: false},
diff --git a/lib/player.js b/lib/player.js
index 2fe0da22b7..a137ace285 100644
--- a/lib/player.js
+++ b/lib/player.js
@@ -6262,6 +6262,18 @@ shaka.Player = class extends shaka.util.FakeEventTarget {
     // change.
     if (this.playhead_) {
       this.playhead_.notifyOfBufferingChange();
+      // Skip the initial buffer gap
+      const startTime = this.mediaSourceEngine_.bufferStart(contentType);
+      if (
+        !this.isLive() &&
+        // If not paused then GapJumpingController will handle this gap.
+        this.video_.paused &&
+        startTime != null &&
+        startTime > 0 &&
+        this.playhead_.getTime() < startTime
+      ) {
+        this.playhead_.setStartTime(startTime);
+      }
     }
     this.pollBufferState_();
 
diff --git a/test/player_integration.js b/test/player_integration.js
index 84956b0cc7..7f95f5e854 100644
--- a/test/player_integration.js
+++ b/test/player_integration.js
@@ -1390,4 +1390,17 @@ describe('Player', () => {
     await video.play();
     await waiter.waitUntilPlayheadReachesOrFailOnTimeout(video, 1, 10);
   });
+
+  describe('buffer gap', () => {
+    // Regression test for issue #6339.
+    it('skip initial buffer gap', async () => {
+      if (window.ManagedMediaSource) {
+        pending('Skipping test, only runs on MSE');
+      }
+      // Ensure the video has loaded.
+      await player.load('/base/test/test/assets/6339/master.mpd');
+      await waiter.timeoutAfter(10).waitForEvent(video, 'loadeddata');
+      expect(video.currentTime).toBeGreaterThanOrEqual(0);
+    });
+  });
 });
diff --git a/test/test/assets/6339/a.mp4 b/test/test/assets/6339/a.mp4
new file mode 100644
index 0000000000..cd2d1af467
Binary files /dev/null and b/test/test/assets/6339/a.mp4 differ
diff --git a/test/test/assets/6339/master.mpd b/test/test/assets/6339/master.mpd
new file mode 100644
index 0000000000..1f259f04ad
--- /dev/null
+++ b/test/test/assets/6339/master.mpd
@@ -0,0 +1,37 @@
+<?xml version="1.0" ?>
+<MPD xmlns="urn:mpeg:dash:schema:mpd:2011" profiles="urn:mpeg:dash:profile:isoff-on-demand:2011" minBufferTime="PT9.98S" mediaPresentationDuration="PT84.00S" type="static">
+	<Period>
+		<AdaptationSet mimeType="video/mp4" segmentAlignment="true" startWithSAP="1"	maxWidth="1280"	maxHeight="720">
+			<Representation id="a4c937bb-6f30-4ecb-8301-09fc1fd94c30" codecs="avc1.4D401F"	width="1280" 	height="720"	scanType="progressive"	frameRate="24" bandwidth="174395">
+				<SegmentList timescale="1000" duration="9982">
+					<Initialization sourceURL="v.mp4" range="36-745"/>
+					<SegmentURL media="v.mp4" mediaRange="746-18481"/>
+					<SegmentURL media="v.mp4" mediaRange="18482-32360"/>
+					<SegmentURL media="v.mp4" mediaRange="32361-46233"/>
+					<SegmentURL media="v.mp4" mediaRange="46234-60106"/>
+					<SegmentURL media="v.mp4" mediaRange="60107-73979"/>
+				</SegmentList>
+			</Representation>
+		</AdaptationSet>
+		<AdaptationSet mimeType="audio/mp4" segmentAlignment="true" startWithSAP="1">
+			<Label>Unknown</Label>
+			<Representation id="b68693a7-abb2-42bb-8d61-3646905df87a" codecs="mp4a.40.2" bandwidth="102962"	audioSamplingRate="44100">
+				<SegmentList timescale="1000" duration="4000">
+					<Initialization sourceURL="a.mp4" range="36-663"/>
+					<SegmentURL media="a.mp4" mediaRange="664-3020"/>
+					<SegmentURL media="a.mp4" mediaRange="3021-5373"/>
+					<SegmentURL media="a.mp4" mediaRange="5374-7713"/>
+					<SegmentURL media="a.mp4" mediaRange="7714-10053"/>
+					<SegmentURL media="a.mp4" mediaRange="10054-12393"/>
+					<SegmentURL media="a.mp4" mediaRange="12394-14746"/>
+					<SegmentURL media="a.mp4" mediaRange="14747-17086"/>
+					<SegmentURL media="a.mp4" mediaRange="17087-19426"/>
+					<SegmentURL media="a.mp4" mediaRange="19427-21766"/>
+					<SegmentURL media="a.mp4" mediaRange="21767-24119"/>
+					<SegmentURL media="a.mp4" mediaRange="24120-26459"/>
+					<SegmentURL media="a.mp4" mediaRange="26460-28799"/>
+				</SegmentList>
+			</Representation>
+		</AdaptationSet>
+	</Period>
+</MPD>
\ No newline at end of file
diff --git a/test/test/assets/6339/v.mp4 b/test/test/assets/6339/v.mp4
new file mode 100644
index 0000000000..49df181c37
Binary files /dev/null and b/test/test/assets/6339/v.mp4 differ