diff --git a/lib/net/http.rb b/lib/net/http.rb
index 41b8357a..d3e0e28e 100644
--- a/lib/net/http.rb
+++ b/lib/net/http.rb
@@ -1103,7 +1103,7 @@ class << HTTP
     # For proxy-defining arguments +p_addr+ through +p_no_proxy+,
     # see {Proxy Server}[rdoc-ref:Net::HTTP@Proxy+Server].
     #
-    def HTTP.new(address, port = nil, p_addr = :ENV, p_port = nil, p_user = nil, p_pass = nil, p_no_proxy = nil)
+    def HTTP.new(address, port = nil, p_addr = :ENV, p_port = nil, p_user = nil, p_pass = nil, p_no_proxy = nil, p_use_ssl = nil)
       http = super address, port
 
       if proxy_class? then # from Net::HTTP::Proxy()
@@ -1112,6 +1112,7 @@ def HTTP.new(address, port = nil, p_addr = :ENV, p_port = nil, p_user = nil, p_p
         http.proxy_port     = @proxy_port
         http.proxy_user     = @proxy_user
         http.proxy_pass     = @proxy_pass
+        http.proxy_use_ssl  = @proxy_use_ssl
       elsif p_addr == :ENV then
         http.proxy_from_env = true
       else
@@ -1123,6 +1124,7 @@ def HTTP.new(address, port = nil, p_addr = :ENV, p_port = nil, p_user = nil, p_p
         http.proxy_port    = p_port || default_port
         http.proxy_user    = p_user
         http.proxy_pass    = p_pass
+        http.proxy_use_ssl = p_use_ssl
       end
 
       http
@@ -1158,6 +1160,7 @@ def initialize(address, port = nil) # :nodoc:
       @proxy_port     = nil
       @proxy_user     = nil
       @proxy_pass     = nil
+      @proxy_use_ssl  = nil
 
       @use_ssl = false
       @ssl_context = nil
@@ -1292,6 +1295,7 @@ def response_body_encoding=(value)
     # Sets the proxy password;
     # see {Proxy Server}[rdoc-ref:Net::HTTP@Proxy+Server].
     attr_writer :proxy_pass
+    attr_writer :proxy_use_ssl
 
     # Returns the IP address for the connection.
     #
@@ -1651,7 +1655,13 @@ def connect
       debug "opened"
       if use_ssl?
         if proxy?
-          plain_sock = BufferedIO.new(s, read_timeout: @read_timeout,
+          if @proxy_use_ssl
+            proxy_sock = OpenSSL::SSL::SSLSocket.new(s)
+            ssl_socket_connect(proxy_sock, @open_timeout)
+          else
+            proxy_sock = s
+          end
+          proxy_sock = BufferedIO.new(proxy_sock, read_timeout: @read_timeout,
                                       write_timeout: @write_timeout,
                                       continue_timeout: @continue_timeout,
                                       debug_output: @debug_output)
@@ -1662,8 +1672,8 @@ def connect
             buf << "Proxy-Authorization: Basic #{credential}\r\n"
           end
           buf << "\r\n"
-          plain_sock.write(buf)
-          HTTPResponse.read_new(plain_sock).value
+          proxy_sock.write(buf)
+          HTTPResponse.read_new(proxy_sock).value
           # assuming nothing left in buffers after successful CONNECT response
         end
 
@@ -1771,13 +1781,14 @@ def do_finish
     @proxy_port = nil
     @proxy_user = nil
     @proxy_pass = nil
+    @proxy_use_ssl = nil
 
     # Creates an \HTTP proxy class which behaves like \Net::HTTP, but
     # performs all access via the specified proxy.
     #
     # This class is obsolete.  You may pass these same parameters directly to
     # \Net::HTTP.new.  See Net::HTTP.new for details of the arguments.
-    def HTTP.Proxy(p_addr = :ENV, p_port = nil, p_user = nil, p_pass = nil) #:nodoc:
+    def HTTP.Proxy(p_addr = :ENV, p_port = nil, p_user = nil, p_pass = nil, p_use_ssl = nil) #:nodoc:
       return self unless p_addr
 
       Class.new(self) {
@@ -1795,6 +1806,7 @@ def HTTP.Proxy(p_addr = :ENV, p_port = nil, p_user = nil, p_pass = nil) #:nodoc:
 
         @proxy_user = p_user
         @proxy_pass = p_pass
+        @proxy_use_ssl = p_use_ssl
       }
     end
 
@@ -1819,6 +1831,9 @@ def proxy_class?
       # Returns the password for accessing the proxy, or +nil+ if none;
       # see Net::HTTP@Proxy+Server.
       attr_reader :proxy_pass
+
+      # Use SSL when talking to the proxy. If Net::HTTP does not use a proxy, nil.
+      attr_reader :proxy_use_ssl
     end
 
     # Returns +true+ if a proxy server is defined, +false+ otherwise;
diff --git a/test/net/http/test_https_proxy.rb b/test/net/http/test_https_proxy.rb
index 4c2a92cc..d7da0cef 100644
--- a/test/net/http/test_https_proxy.rb
+++ b/test/net/http/test_https_proxy.rb
@@ -43,5 +43,53 @@ def test_https_proxy_authentication
       assert_join_threads([client_thread, server_thread])
     }
   end
+
+  def test_https_proxy_ssl_connection
+    begin
+      OpenSSL
+    rescue LoadError
+      omit 'autoload problem. see [ruby-dev:45021][Bug #5786]'
+    end
+
+    tcpserver = TCPServer.new("127.0.0.1", 0)
+    ctx = OpenSSL::SSL::SSLContext.new
+    ctx.key = OpenSSL::PKey::RSA.new 2048
+    ctx.cert = OpenSSL::X509::Certificate.new
+    ctx.cert.subject = OpenSSL::X509::Name.new [['CN', 'localhost']]
+    ctx.cert.issuer = ctx.cert.subject
+    ctx.cert.public_key = ctx.key
+    ctx.cert.not_before = Time.now
+    ctx.cert.not_after = Time.now + 60 * 60 * 24
+    ctx.cert.sign ctx.key, OpenSSL::Digest::SHA1.new
+    serv = OpenSSL::SSL::SSLServer.new(tcpserver, ctx)
+
+    _, port, _, _ = serv.addr
+    client_thread = Thread.new {
+      proxy = Net::HTTP.Proxy("127.0.0.1", port, 'user', 'password', true)
+      http = proxy.new("foo.example.org", 8000)
+      http.use_ssl = true
+      http.verify_mode = OpenSSL::SSL::VERIFY_NONE
+      begin
+        http.start
+      rescue EOFError
+      end
+    }
+    server_thread = Thread.new {
+      sock = serv.accept
+      begin
+        proxy_request = sock.gets("\r\n\r\n")
+        assert_equal(
+          "CONNECT foo.example.org:8000 HTTP/1.1\r\n" +
+          "Host: foo.example.org:8000\r\n" +
+          "Proxy-Authorization: Basic dXNlcjpwYXNzd29yZA==\r\n" +
+          "\r\n",
+          proxy_request,
+          "[ruby-core:96672]")
+      ensure
+        sock.close
+      end
+    }
+    assert_join_threads([client_thread, server_thread])
+  end
 end if defined?(OpenSSL)