diff --git a/http2/frame.go b/http2/frame.go
index 81faec7..97bd8b0 100644
--- a/http2/frame.go
+++ b/http2/frame.go
@@ -225,6 +225,11 @@
 	},
 }
 
+func invalidHTTP1LookingFrameHeader() FrameHeader {
+	fh, _ := readFrameHeader(make([]byte, frameHeaderLen), strings.NewReader("HTTP/1.1 "))
+	return fh
+}
+
 // ReadFrameHeader reads 9 bytes from r and returns a FrameHeader.
 // Most users should use Framer.ReadFrame instead.
 func ReadFrameHeader(r io.Reader) (FrameHeader, error) {
@@ -503,10 +508,16 @@
 		return nil, err
 	}
 	if fh.Length > fr.maxReadSize {
+		if fh == invalidHTTP1LookingFrameHeader() {
+			return nil, fmt.Errorf("http2: failed reading the frame payload: %w, note that the frame header looked like an HTTP/1.1 header", err)
+		}
 		return nil, ErrFrameTooLarge
 	}
 	payload := fr.getReadBuf(fh.Length)
 	if _, err := io.ReadFull(fr.r, payload); err != nil {
+		if fh == invalidHTTP1LookingFrameHeader() {
+			return nil, fmt.Errorf("http2: failed reading the frame payload: %w, note that the frame header looked like an HTTP/1.1 header", err)
+		}
 		return nil, err
 	}
 	f, err := typeFrameParser(fh.Type)(fr.frameCache, fh, fr.countError, payload)
diff --git a/http2/transport_test.go b/http2/transport_test.go
index 1eeb76e..596499f 100644
--- a/http2/transport_test.go
+++ b/http2/transport_test.go
@@ -272,6 +272,48 @@
 	}
 }
 
+func TestTransportFailureErrorForHTTP1Response(t *testing.T) {
+	const expectedHTTP1PayloadHint = "frame header looked like an HTTP/1.1 header"
+
+	ts := httptest.NewServer(http.NewServeMux())
+	t.Cleanup(ts.Close)
+
+	for _, tc := range []struct {
+		name            string
+		maxFrameSize    uint32
+		expectedErrorIs error
+	}{
+		{
+			name:         "with default max frame size",
+			maxFrameSize: 0,
+		},
+		{
+			name:         "with enough frame size to start reading",
+			maxFrameSize: invalidHTTP1LookingFrameHeader().Length + 1,
+		},
+	} {
+		t.Run(tc.name, func(t *testing.T) {
+			tr := &Transport{
+				DialTLSContext: func(ctx context.Context, network, addr string, cfg *tls.Config) (net.Conn, error) {
+					return net.Dial(network, addr)
+				},
+				MaxReadFrameSize: tc.maxFrameSize,
+				AllowHTTP:        true,
+			}
+
+			req, err := http.NewRequest("GET", ts.URL, nil)
+			if err != nil {
+				t.Fatal(err)
+			}
+
+			_, err = tr.RoundTrip(req)
+			if !strings.Contains(err.Error(), expectedHTTP1PayloadHint) {
+				t.Errorf("expected error to contain %q, got %v", expectedHTTP1PayloadHint, err)
+			}
+		})
+	}
+}
+
 func testTransportReusesConns(t *testing.T, useClient, wantSame bool, modReq func(*http.Request)) {
 	ts := newTestServer(t, func(w http.ResponseWriter, r *http.Request) {
 		io.WriteString(w, r.RemoteAddr)