diff --git a/src/net/mail/message.go b/src/net/mail/message.go
index 6268c08f47..a416007fdb 100644
--- a/src/net/mail/message.go
+++ b/src/net/mail/message.go
@@ -54,7 +54,7 @@ func ReadMessage(r io.Reader) (msg *Message, err error) {
 	tp := textproto.NewReader(bufio.NewReader(r))
 
 	hdr, err := tp.ReadMIMEHeader()
-	if err != nil {
+	if err != nil && (err != io.EOF || len(hdr) == 0) {
 		return nil, err
 	}
 
diff --git a/src/net/mail/message_test.go b/src/net/mail/message_test.go
index 61e50ccfd5..4b581ccc73 100644
--- a/src/net/mail/message_test.go
+++ b/src/net/mail/message_test.go
@@ -39,6 +39,19 @@ So, "Hello".
 		},
 		body: "This is a message just to say hello.\nSo, \"Hello\".\n",
 	},
+	{
+		// RFC 5965, Appendix B.1, a part of the multipart message (a header-only sub message)
+		in: `Feedback-Type: abuse
+User-Agent: SomeGenerator/1.0
+Version: 1
+`,
+		header: Header{
+			"Feedback-Type": []string{"abuse"},
+			"User-Agent":    []string{"SomeGenerator/1.0"},
+			"Version":       []string{"1"},
+		},
+		body: "",
+	},
 }
 
 func TestParsing(t *testing.T) {