diff --git a/client.go b/client.go
index 170301d..9b6e18a 100644
--- a/client.go
+++ b/client.go
@@ -303,7 +303,9 @@ func (d *Dialer) DialContext(ctx context.Context, urlStr string, requestHeader h
 			return nil, nil, err
 		}
 		if proxyURL != nil {
-			dialer, err := proxy_FromURL(proxyURL, netDialerFunc(netDial))
+			proxyDialer := &netDialerFunc{fn: netDial}
+			modifyProxyDialer(ctx, d, proxyURL, proxyDialer)
+			dialer, err := proxy_FromURL(proxyURL, proxyDialer)
 			if err != nil {
 				return nil, nil, err
 			}
diff --git a/client_server_httpsproxy_test.go b/client_server_httpsproxy_test.go
new file mode 100644
index 0000000..71f0d55
--- /dev/null
+++ b/client_server_httpsproxy_test.go
@@ -0,0 +1,52 @@
+//go:build go1.15
+// +build go1.15
+
+package websocket
+
+import (
+	"crypto/tls"
+	"net/http"
+	"net/url"
+	"testing"
+)
+
+func TestHttpsProxy(t *testing.T) {
+
+	sTLS := newTLSServer(t)
+	defer sTLS.Close()
+	s := newServer(t)
+	defer s.Close()
+
+	surlTLS, _ := url.Parse(sTLS.Server.URL)
+
+	cstDialer := cstDialer // make local copy for modification on next line.
+	cstDialer.Proxy = http.ProxyURL(surlTLS)
+
+	connect := false
+	origHandler := sTLS.Server.Config.Handler
+
+	// Capture the request Host header.
+	sTLS.Server.Config.Handler = http.HandlerFunc(
+		func(w http.ResponseWriter, r *http.Request) {
+			if r.Method == "CONNECT" {
+				connect = true
+				w.WriteHeader(http.StatusOK)
+				return
+			}
+
+			if !connect {
+				t.Log("connect not received")
+				http.Error(w, "connect not received", http.StatusMethodNotAllowed)
+				return
+			}
+			origHandler.ServeHTTP(w, r)
+		})
+
+	cstDialer.TLSClientConfig = &tls.Config{RootCAs: rootCAs(t, sTLS.Server)}
+	ws, _, err := cstDialer.Dial(s.URL, nil)
+	if err != nil {
+		t.Fatalf("Dial: %v", err)
+	}
+	defer ws.Close()
+	sendRecv(t, ws)
+}
diff --git a/proxy.go b/proxy.go
index 18abf6e..a370b31 100644
--- a/proxy.go
+++ b/proxy.go
@@ -15,21 +15,37 @@ import (
 	"strings"
 )
 
-type netDialerFunc func(network, addr string) (net.Conn, error)
+// proxyDialerEx extends the generated proxy_Dialer
+type proxyDialerEx interface {
+	proxy_Dialer
+	// UsesTLS indicates whether we expect to dial to a TLS proxy
+	UsesTLS() bool
+}
 
-func (fn netDialerFunc) Dial(network, addr string) (net.Conn, error) {
-	return fn(network, addr)
+type netDialerFunc struct {
+	fn      func(network, addr string) (net.Conn, error)
+	usesTLS bool
+}
+
+func (ndf *netDialerFunc) Dial(network, addr string) (net.Conn, error) {
+	return ndf.fn(network, addr)
+}
+
+func (ndf *netDialerFunc) UsesTLS() bool {
+	return ndf.usesTLS
 }
 
 func init() {
 	proxy_RegisterDialerType("http", func(proxyURL *url.URL, forwardDialer proxy_Dialer) (proxy_Dialer, error) {
-		return &httpProxyDialer{proxyURL: proxyURL, forwardDial: forwardDialer.Dial}, nil
+		return &httpProxyDialer{proxyURL: proxyURL, forwardDial: forwardDialer.Dial, usesTLS: false}, nil
 	})
+	registerDialerHttps()
 }
 
 type httpProxyDialer struct {
 	proxyURL    *url.URL
 	forwardDial func(network, addr string) (net.Conn, error)
+	usesTLS     bool
 }
 
 func (hpd *httpProxyDialer) Dial(network string, addr string) (net.Conn, error) {
@@ -86,3 +102,7 @@ func (hpd *httpProxyDialer) Dial(network string, addr string) (net.Conn, error)
 	}
 	return conn, nil
 }
+
+func (hpd *httpProxyDialer) UsesTLS() bool {
+	return hpd.usesTLS
+}
diff --git a/proxy_https.go b/proxy_https.go
new file mode 100644
index 0000000..f74258a
--- /dev/null
+++ b/proxy_https.go
@@ -0,0 +1,37 @@
+//go:build go1.15
+// +build go1.15
+
+package websocket
+
+import (
+	"context"
+	"crypto/tls"
+	"net"
+	"net/url"
+)
+
+func registerDialerHttps() {
+	proxy_RegisterDialerType("https", func(proxyURL *url.URL, forwardDialer proxy_Dialer) (proxy_Dialer, error) {
+		fwd := forwardDialer.Dial
+		if dialerEx, ok := forwardDialer.(proxyDialerEx); !ok || !dialerEx.UsesTLS() {
+			tlsDialer := &tls.Dialer{
+				Config:    &tls.Config{},
+				NetDialer: &net.Dialer{},
+			}
+			fwd = tlsDialer.Dial
+		}
+		return &httpProxyDialer{proxyURL: proxyURL, forwardDial: fwd, usesTLS: true}, nil
+	})
+}
+
+func modifyProxyDialer(ctx context.Context, d *Dialer, proxyURL *url.URL, proxyDialer *netDialerFunc) {
+	if proxyURL.Scheme == "https" {
+		proxyDialer.usesTLS = true
+		proxyDialer.fn = func(network, addr string) (net.Conn, error) {
+			t := tls.Dialer{}
+			t.Config = d.TLSClientConfig
+			t.NetDialer = &net.Dialer{}
+			return t.DialContext(ctx, network, addr)
+		}
+	}
+}
diff --git a/proxy_https_legacy.go b/proxy_https_legacy.go
new file mode 100644
index 0000000..40bc5e2
--- /dev/null
+++ b/proxy_https_legacy.go
@@ -0,0 +1,15 @@
+//go:build !go1.15
+// +build !go1.15
+
+package websocket
+
+import (
+	"context"
+	"net/url"
+)
+
+func registerDialerHttps() {
+}
+
+func modifyProxyDialer(ctx context.Context, d *Dialer, proxyURL *url.URL, proxyDialer *netDialerFunc) {
+}