diff --git a/README.md b/README.md
index 02831dac..aebb701b 100644
--- a/README.md
+++ b/README.md
@@ -119,6 +119,7 @@ Check out the **[contributing wiki](https://github.com/pion/webrtc/wiki/Contribu
 * [Alex Harford](https://github.com/alexjh)
 * [Aleksandr Razumov](https://github.com/ernado)
 * [mchlrhw](https://github.com/mchlrhw)
+* [AlexWoo(武杰)](https://github.com/AlexWoo) *Fix RemoteDescription parsing for certificate fingerprint*
 
 ### License
 MIT License - see [LICENSE](LICENSE) for full text
diff --git a/peerconnection.go b/peerconnection.go
index 374ffae6..bf6d30ce 100644
--- a/peerconnection.go
+++ b/peerconnection.go
@@ -874,7 +874,12 @@ func (pc *PeerConnection) SetRemoteDescription(desc SessionDescription) error {
 		weOffer = false
 	}
 
+	fingerprint, haveFingerprint := desc.parsed.Attribute("fingerprint")
 	for _, m := range pc.RemoteDescription().parsed.MediaDescriptions {
+		if !haveFingerprint {
+			fingerprint, haveFingerprint = m.Attribute("fingerprint")
+		}
+
 		for _, a := range m.Attributes {
 			switch {
 			case a.IsICECandidate():
@@ -899,20 +904,16 @@ func (pc *PeerConnection) SetRemoteDescription(desc SessionDescription) error {
 		}
 	}
 
-	fingerprint, ok := desc.parsed.Attribute("fingerprint")
-	if !ok {
-		fingerprint, ok = desc.parsed.MediaDescriptions[0].Attribute("fingerprint")
-		if !ok {
-			return fmt.Errorf("could not find fingerprint")
-		}
+	if !haveFingerprint {
+		return fmt.Errorf("could not find fingerprint")
 	}
-	var fingerprintHash string
+
 	parts := strings.Split(fingerprint, " ")
 	if len(parts) != 2 {
 		return fmt.Errorf("invalid fingerprint")
 	}
 	fingerprint = parts[1]
-	fingerprintHash = parts[0]
+	fingerprintHash := parts[0]
 
 	// Create the SCTP transport
 	sctp := pc.api.NewSCTPTransport(pc.dtlsTransport)
diff --git a/peerconnection_test.go b/peerconnection_test.go
index 86f93c97..487c2bcc 100644
--- a/peerconnection_test.go
+++ b/peerconnection_test.go
@@ -418,3 +418,44 @@ func TestMultipleOfferAnswer(t *testing.T) {
 		t.Errorf("Second Offer: got error: %v", err)
 	}
 }
+
+func TestNoFingerprintInFirstMediaIfSetRemoteDescription(t *testing.T) {
+	const sdpNoFingerprintInFirstMedia = `v=0
+o=- 143087887 1561022767 IN IP4 192.168.84.254
+s=VideoRoom 404986692241682
+t=0 0
+a=group:BUNDLE audio
+a=msid-semantic: WMS 2867270241552712
+m=video 0 UDP/TLS/RTP/SAVPF 0
+c=IN IP4 192.168.84.254
+a=inactive
+m=audio 9 UDP/TLS/RTP/SAVPF 111
+c=IN IP4 192.168.84.254
+a=recvonly
+a=mid:audio
+a=rtcp-mux
+a=ice-ufrag:AS/w
+a=ice-pwd:9NOgoAOMALYu/LOpA1iqg/
+a=ice-options:trickle
+a=fingerprint:sha-256 D2:B9:31:8F:DF:24:D8:0E:ED:D2:EF:25:9E:AF:6F:B8:34:AE:53:9C:E6:F3:8F:F2:64:15:FA:E8:7F:53:2D:38
+a=setup:active
+a=rtpmap:111 opus/48000/2
+a=candidate:1 1 udp 2013266431 192.168.84.254 46492 typ host
+a=end-of-candidates
+`
+
+	pc, err := NewPeerConnection(Configuration{})
+	if err != nil {
+		t.Error(err.Error())
+	}
+
+	desc := SessionDescription{
+		Type: SDPTypeOffer,
+		SDP:  sdpNoFingerprintInFirstMedia,
+	}
+
+	err = pc.SetRemoteDescription(desc)
+	if err != nil {
+		t.Error(err.Error())
+	}
+}