diff --git a/client.go b/client.go
index 0df5c31..0dc5119 100644
--- a/client.go
+++ b/client.go
@@ -256,8 +256,16 @@ func (d *Dialer) DialContext(ctx context.Context, urlStr string, requestHeader h
 		}
 		if proxyURL != nil {
 			forwardDial := newNetDialerFunc(proxyURL.Scheme, d.NetDial, d.NetDialContext, d.NetDialTLSContext)
-			if proxyURL.Scheme == "http" || proxyURL.Scheme == "https" {
-				netDial = newHTTPProxyDialerFunc(proxyURL, forwardDial)
+			if proxyURL.Scheme == "https" && d.NetDialTLSContext == nil {
+				tlsClientConfig := cloneTLSConfig(d.TLSClientConfig)
+				if d.TLSClientConfig == nil {
+					tlsClientConfig = &tls.Config{
+						ServerName: proxyURL.Hostname(),
+					}
+				}
+				netDial = newHTTPProxyDialerFunc(proxyURL, forwardDial, tlsClientConfig)
+			} else if proxyURL.Scheme == "http" || proxyURL.Scheme == "https" {
+				netDial = newHTTPProxyDialerFunc(proxyURL, forwardDial, nil)
 			} else {
 				dialer, err := proxy.FromURL(proxyURL, forwardDial)
 				if err != nil {
diff --git a/proxy.go b/proxy.go
index 8638ab0..c3c0e45 100644
--- a/proxy.go
+++ b/proxy.go
@@ -8,6 +8,7 @@ import (
 	"bufio"
 	"bytes"
 	"context"
+	"crypto/tls"
 	"encoding/base64"
 	"errors"
 	"net"
@@ -46,7 +47,11 @@ func (fn netDialerFunc) DialContext(ctx context.Context, network, addr string) (
 	return fn(ctx, network, addr)
 }
 
-func newHTTPProxyDialerFunc(proxyURL *url.URL, forwardDial netDialerFunc) netDialerFunc {
+// newHTTPProxyDialerFunc returns a netDialerFunc that dials using the provided
+// proxyURL. The forwardDial function is used to establish the connection to the
+// proxy server. If tlsClientConfig is not nil, the connection to the proxy is
+// upgraded to a TLS connection with tls.Client.
+func newHTTPProxyDialerFunc(proxyURL *url.URL, forwardDial netDialerFunc, tlsClientConfig *tls.Config) netDialerFunc {
 	return func(ctx context.Context, network, addr string) (net.Conn, error) {
 		hostPort, _ := hostPortNoPort(proxyURL)
 		conn, err := forwardDial(ctx, network, hostPort)
@@ -54,6 +59,14 @@ func newHTTPProxyDialerFunc(proxyURL *url.URL, forwardDial netDialerFunc) netDia
 			return nil, err
 		}
 
+		if tlsClientConfig != nil {
+			tlsConn := tls.Client(conn, tlsClientConfig)
+			if err = tlsConn.HandshakeContext(ctx); err != nil {
+				return nil, err
+			}
+			conn = tlsConn
+		}
+
 		connectHeader := make(http.Header)
 		if user := proxyURL.User; user != nil {
 			proxyUser := user.Username()