diff --git a/.changes/nextrelease/retry_curl35.json b/.changes/nextrelease/retry_curl35.json
new file mode 100644
index 0000000000..309440917c
--- /dev/null
+++ b/.changes/nextrelease/retry_curl35.json
@@ -0,0 +1,7 @@
+[
+  {
+    "type": "enhancement",
+    "category": "",
+    "description": "Enables retries of the CURLE_SSL_CONNECT_ERROR (35) failure."
+  }
+]
diff --git a/src/RetryMiddleware.php b/src/RetryMiddleware.php
index 4fa81e9871..019fe1dc74 100644
--- a/src/RetryMiddleware.php
+++ b/src/RetryMiddleware.php
@@ -80,6 +80,7 @@ public static function createDefaultDecider(
     ) {
         $retryCurlErrors = [];
         if (extension_loaded('curl')) {
+            $retryCurlErrors[CURLE_SSL_CONNECT_ERROR] = true;
             $retryCurlErrors[CURLE_RECV_ERROR] = true;
         }
 
diff --git a/tests/RetryMiddlewareTest.php b/tests/RetryMiddlewareTest.php
index 9f64b0e35a..7d72f1b1fa 100644
--- a/tests/RetryMiddlewareTest.php
+++ b/tests/RetryMiddlewareTest.php
@@ -84,7 +84,12 @@ public function testDeciderIgnoresPHPError()
         }
     }
 
-    public function testDeciderRetriesWhenCurlErrorCodeMatches()
+    /**
+     * @param int $curlErrorCode
+     * @param bool $expected
+     * @dataProvider curlErrorCodesProvider
+     */
+    public function testDeciderRetriesWhenCurlErrorCodeMatches($curlErrorCode, $expected)
     {
         if (!extension_loaded('curl')) {
             $this->markTestSkipped('Test skipped on no cURL extension');
@@ -99,11 +104,11 @@ public function testDeciderRetriesWhenCurlErrorCodeMatches()
                 $request,
                 null,
                 null,
-                ['errno' => CURLE_RECV_ERROR]
+                ['errno' => $curlErrorCode]
             );
         } elseif ($version === 5) {
             $previous = new RequestException(
-                'cURL error ' . CURLE_RECV_ERROR . ': test',
+                'cURL error ' . $curlErrorCode . ': test',
                 new \GuzzleHttp\Message\Request('GET', 'http://www.example.com')
             );
         }
@@ -113,7 +118,16 @@ public function testDeciderRetriesWhenCurlErrorCodeMatches()
             ['connection_error' => false],
             $previous
         );
-        $this->assertTrue($decider(0, $command, $request, null, $err));
+        $this->assertEquals($expected, $decider(0, $command, $request, null, $err));
+    }
+
+    public static function curlErrorCodesProvider()
+    {
+        return [
+            'Error 35 should retry' => [CURLE_SSL_CONNECT_ERROR, true],
+            'Error 56 should retry' => [CURLE_RECV_ERROR, true],
+            'Error 0 should not retry' => [CURLE_OK, false],
+        ];
     }
 
     public function testDeciderRetriesForCustomCurlErrors()