diff --git a/Doc/library/ssl.rst b/Doc/library/ssl.rst
index 1cfd165202d..1adac843f4e 100644
--- a/Doc/library/ssl.rst
+++ b/Doc/library/ssl.rst
@@ -634,6 +634,13 @@ Constants
 
    .. versionadded:: 3.4
 
+.. data:: VERIFY_ALLOW_PROXY_CERTS
+
+   Possible value for :attr:`SSLContext.verify_flags` to enables proxy
+   certificate verification.
+
+   .. versionadded:: 3.10
+
 .. data:: VERIFY_X509_TRUSTED_FIRST
 
    Possible value for :attr:`SSLContext.verify_flags`. It instructs OpenSSL to
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 67850c34e00..1710dda4389 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1305,6 +1305,8 @@ def test_verify_flags(self):
         self.assertEqual(ctx.verify_flags, ssl.VERIFY_CRL_CHECK_CHAIN)
         ctx.verify_flags = ssl.VERIFY_DEFAULT
         self.assertEqual(ctx.verify_flags, ssl.VERIFY_DEFAULT)
+        ctx.verify_flags = ssl.VERIFY_ALLOW_PROXY_CERTS
+        self.assertEqual(ctx.verify_flags, ssl.VERIFY_ALLOW_PROXY_CERTS)
         # supports any value
         ctx.verify_flags = ssl.VERIFY_CRL_CHECK_LEAF | ssl.VERIFY_X509_STRICT
         self.assertEqual(ctx.verify_flags,
diff --git a/Misc/NEWS.d/next/Library/2020-01-15-11-15-35.bpo-39342.S8PuJO.rst b/Misc/NEWS.d/next/Library/2020-01-15-11-15-35.bpo-39342.S8PuJO.rst
new file mode 100644
index 00000000000..6eb83a95b5e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-01-15-11-15-35.bpo-39342.S8PuJO.rst
@@ -0,0 +1,4 @@
+Expose ``X509_V_FLAG_ALLOW_PROXY_CERTS`` as
+:data:`~ssl.VERIFY_ALLOW_PROXY_CERTS` to allow proxy certificate validation
+as explained in
+https://www.openssl.org/docs/man1.1.1/man7/proxy-certificates.html.
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 96d2796fcfa..bea144cd9f9 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -6181,6 +6181,8 @@ sslmodule_init_constants(PyObject *m)
                             X509_V_FLAG_CRL_CHECK|X509_V_FLAG_CRL_CHECK_ALL);
     PyModule_AddIntConstant(m, "VERIFY_X509_STRICT",
                             X509_V_FLAG_X509_STRICT);
+    PyModule_AddIntConstant(m, "VERIFY_ALLOW_PROXY_CERTS",
+                            X509_V_FLAG_ALLOW_PROXY_CERTS);
 #ifdef X509_V_FLAG_TRUSTED_FIRST
     PyModule_AddIntConstant(m, "VERIFY_X509_TRUSTED_FIRST",
                             X509_V_FLAG_TRUSTED_FIRST);