diff --git a/Cargo.toml b/Cargo.toml
index cab1d47..4193117 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -24,7 +24,7 @@ libc = "0.2"
 tempfile = "3.1.0"
 
 [target.'cfg(target_os = "windows")'.dependencies]
-schannel = "0.1.17"
+schannel = "0.1.20"
 
 [target.'cfg(not(any(target_os = "windows", target_os = "macos", target_os = "ios")))'.dependencies]
 log = "0.4.5"
diff --git a/build.rs b/build.rs
index b7a41f4..4f9f63b 100644
--- a/build.rs
+++ b/build.rs
@@ -8,6 +8,11 @@ fn main() {
         if version >= 0x1_01_00_00_0 {
             println!("cargo:rustc-cfg=have_min_max_version");
         }
+
+        // TLS 1.3 requires openssl 1.1.1
+        if version >= 0x1_01_01_00_0 {
+            println!("cargo:rustc-cfg=have_tls13_version");
+        }
     }
 
     if let Ok(version) = env::var("DEP_OPENSSL_LIBRESSL_VERSION_NUMBER") {
@@ -16,5 +21,10 @@ fn main() {
         if version >= 0x2_06_01_00_0 {
             println!("cargo:rustc-cfg=have_min_max_version");
         }
+
+        // TLS 1.3 requires libressl 3.4.0
+        if version >= 0x3_04_00_00_0 {
+            println!("cargo:rustc-cfg=have_tls13_version");
+        }
     }
 }
diff --git a/src/imp/openssl.rs b/src/imp/openssl.rs
index 8fc4362..b318b7c 100644
--- a/src/imp/openssl.rs
+++ b/src/imp/openssl.rs
@@ -23,20 +23,24 @@ fn supported_protocols(
     min: Option<Protocol>,
     max: Option<Protocol>,
     ctx: &mut SslContextBuilder,
-) -> Result<(), ErrorStack> {
+) -> Result<(), Error> {
     use self::openssl::ssl::SslVersion;
 
-    fn cvt(p: Protocol) -> SslVersion {
+    fn cvt(p: Protocol) -> Result<SslVersion, Error> {
         match p {
-            Protocol::Sslv3 => SslVersion::SSL3,
-            Protocol::Tlsv10 => SslVersion::TLS1,
-            Protocol::Tlsv11 => SslVersion::TLS1_1,
-            Protocol::Tlsv12 => SslVersion::TLS1_2,
+            Protocol::Sslv3 => Ok(SslVersion::SSL3),
+            Protocol::Tlsv10 => Ok(SslVersion::TLS1),
+            Protocol::Tlsv11 => Ok(SslVersion::TLS1_1),
+            Protocol::Tlsv12 => Ok(SslVersion::TLS1_2),
+            #[cfg(have_tls13_version)]
+            Protocol::Tlsv13 => Ok(SslVersion::TLS1_3),
+            #[cfg(not(have_tls13_version))]
+            Protocol::Tlsv13 => Err(Error::UnsupportedTls13)
         }
     }
 
-    ctx.set_min_proto_version(min.map(cvt))?;
-    ctx.set_max_proto_version(max.map(cvt))?;
+    ctx.set_min_proto_version(min.map(cvt).transpose()?)?;
+    ctx.set_max_proto_version(max.map(cvt).transpose()?)?;
 
     Ok(())
 }
@@ -115,6 +119,7 @@ pub enum Error {
     Ssl(ssl::Error, X509VerifyResult),
     EmptyChain,
     NotPkcs8,
+    UnsupportedTls13,
 }
 
 impl error::Error for Error {
@@ -124,6 +129,7 @@ impl error::Error for Error {
             Error::Ssl(ref e, _) => error::Error::source(e),
             Error::EmptyChain => None,
             Error::NotPkcs8 => None,
+            Error::UnsupportedTls13 => None,
         }
     }
 }
@@ -139,6 +145,7 @@ impl fmt::Display for Error {
                 "at least one certificate must be provided to create an identity"
             ),
             Error::NotPkcs8 => write!(fmt, "expected PKCS#8 PEM"),
+            Error::UnsupportedTls13 => write!(fmt, "TLS version 1.3 not supported"),
         }
     }
 }
diff --git a/src/imp/schannel.rs b/src/imp/schannel.rs
index 62e5042..faeb5dc 100644
--- a/src/imp/schannel.rs
+++ b/src/imp/schannel.rs
@@ -19,6 +19,7 @@ static PROTOCOLS: &'static [Protocol] = &[
     Protocol::Tls10,
     Protocol::Tls11,
     Protocol::Tls12,
+    Protocol::Tls13,
 ];
 
 fn convert_protocols(min: Option<::Protocol>, max: Option<::Protocol>) -> &'static [Protocol] {
diff --git a/src/imp/security_framework.rs b/src/imp/security_framework.rs
index f56a916..b5366ee 100644
--- a/src/imp/security_framework.rs
+++ b/src/imp/security_framework.rs
@@ -43,12 +43,14 @@ static SET_AT_EXIT: Once = Once::new();
 #[cfg(not(target_os = "ios"))]
 static TEMP_KEYCHAIN: Lazy<Mutex<Option<(SecKeychain, TempDir)>>> = Lazy::new(|| Mutex::new(None));
 
-fn convert_protocol(protocol: Protocol) -> SslProtocol {
+fn convert_protocol(protocol: Protocol) -> Result<SslProtocol, Error> {
     match protocol {
-        Protocol::Sslv3 => SslProtocol::SSL3,
-        Protocol::Tlsv10 => SslProtocol::TLS1,
-        Protocol::Tlsv11 => SslProtocol::TLS11,
-        Protocol::Tlsv12 => SslProtocol::TLS12,
+        Protocol::Sslv3 => Ok(SslProtocol::SSL3),
+        Protocol::Tlsv10 => Ok(SslProtocol::TLS1),
+        Protocol::Tlsv11 => Ok(SslProtocol::TLS11),
+        Protocol::Tlsv12 => Ok(SslProtocol::TLS12),
+        // Not supported in SecureTransport API used in security_framework
+        Protocol::Tlsv13 => Err(Error(base::Error::from("TLS 1.3 is not supported")))
     }
 }
 
diff --git a/src/lib.rs b/src/lib.rs
index 267679d..e10d664 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -322,6 +322,11 @@ pub enum Protocol {
     Tlsv11,
     /// The TLS 1.2 protocol.
     Tlsv12,
+    /// The TLS 1.3 protocol.
+    ///
+    /// Only works on Windows, or with openssl >= 1.1.1 or libressl >= 3.4.0.
+    /// It will fail at runtime when used in other situations.
+    Tlsv13,
 }
 
 /// A builder for `TlsConnector`s.
diff --git a/src/test.rs b/src/test.rs
index c51b0bc..05beb1e 100644
--- a/src/test.rs
+++ b/src/test.rs
@@ -16,6 +16,26 @@ macro_rules! p {
     };
 }
 
+#[cfg(any(target_os = "windows", have_tls13_version))]
+#[test]
+fn connect_google_tls13() {
+    let builder = p!(
+            TlsConnector::builder()
+            .min_protocol_version(Some(Protocol::Tlsv13))
+            .max_protocol_version(Some(Protocol::Tlsv13))
+            .build());
+    let s = p!(TcpStream::connect("google.com:443"));
+    let mut socket = p!(builder.connect("google.com", s));
+
+    p!(socket.write_all(b"GET / HTTP/1.0\r\n\r\n"));
+    let mut result = vec![];
+    p!(socket.read_to_end(&mut result));
+
+    println!("{}", String::from_utf8_lossy(&result));
+    assert!(result.starts_with(b"HTTP/1.0"));
+    assert!(result.ends_with(b"</HTML>\r\n") || result.ends_with(b"</html>"));
+}
+
 #[test]
 fn connect_google() {
     let builder = p!(TlsConnector::new());