diff --git a/setup.cfg b/setup.cfg
index 33c3e95a3..6a22be6b1 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -82,7 +82,7 @@ plugins =
 
 [coverage:report]
 precision = 2
-fail_under = 97.69
+fail_under = 97.63
 show_missing = true
 skip_covered = true
 exclude_lines =
diff --git a/uvicorn/protocols/http/h11_impl.py b/uvicorn/protocols/http/h11_impl.py
index 5fff70bb7..821416f4b 100644
--- a/uvicorn/protocols/http/h11_impl.py
+++ b/uvicorn/protocols/http/h11_impl.py
@@ -204,12 +204,18 @@ def handle_events(self) -> None:
                     "headers": self.headers,
                 }
 
+                is_upgrade, is_http2 = False, False
                 for name, value in self.headers:
                     if name == b"connection":
                         tokens = [token.lower().strip() for token in value.split(b",")]
                         if b"upgrade" in tokens:
-                            self.handle_upgrade(event)
-                            return
+                            is_upgrade = True
+                    elif name == b"upgrade" and value == b"h2c":
+                        is_http2 = True
+
+                if is_upgrade and not is_http2:
+                    self.handle_upgrade(event)
+                    return
 
                 # Handle 503 responses when 'limit_concurrency' is exceeded.
                 if self.limit_concurrency is not None and (
diff --git a/uvicorn/protocols/http/httptools_impl.py b/uvicorn/protocols/http/httptools_impl.py
index f018c59af..82ee00924 100644
--- a/uvicorn/protocols/http/httptools_impl.py
+++ b/uvicorn/protocols/http/httptools_impl.py
@@ -104,6 +104,7 @@ def __init__(
         self.scope: HTTPScope = None  # type: ignore[assignment]
         self.headers: List[Tuple[bytes, bytes]] = None  # type: ignore[assignment]
         self.expect_100_continue = False
+        self.is_http2 = False
         self.cycle: RequestResponseCycle = None  # type: ignore[assignment]
 
     # Protocol interface
@@ -168,7 +169,9 @@ def handle_upgrade(self) -> None:
             if name == b"upgrade":
                 upgrade_value = value.lower()
 
-        if upgrade_value != b"websocket" or self.ws_protocol_class is None:
+        if upgrade_value == b"h2c":
+            return
+        elif upgrade_value != b"websocket" or self.ws_protocol_class is None:
             msg = "Unsupported upgrade request."
             self.logger.warning(msg)
             from uvicorn.protocols.websockets.auto import AutoWebSocketsProtocol
@@ -236,6 +239,8 @@ def on_header(self, name: bytes, value: bytes) -> None:
         name = name.lower()
         if name == b"expect" and value.lower() == b"100-continue":
             self.expect_100_continue = True
+        elif name == b"upgrade" and value == b"h2c":
+            self.is_http2 = True
         self.headers.append((name, value))
 
     def on_headers_complete(self) -> None:
@@ -244,7 +249,7 @@ def on_headers_complete(self) -> None:
         self.scope["method"] = method.decode("ascii")
         if http_version != "1.1":
             self.scope["http_version"] = http_version
-        if self.parser.should_upgrade():
+        if self.parser.should_upgrade() and not self.is_http2:
             return
         parsed_url = httptools.parse_url(self.url)
         raw_path = parsed_url.path
@@ -291,7 +296,9 @@ def on_headers_complete(self) -> None:
             self.pipeline.appendleft((self.cycle, app))
 
     def on_body(self, body: bytes) -> None:
-        if self.parser.should_upgrade() or self.cycle.response_complete:
+        if (
+            self.parser.should_upgrade() and not self.is_http2
+        ) or self.cycle.response_complete:
             return
         self.cycle.body += body
         if len(self.cycle.body) > HIGH_WATER_LIMIT:
@@ -299,7 +306,9 @@ def on_body(self, body: bytes) -> None:
         self.cycle.message_event.set()
 
     def on_message_complete(self) -> None:
-        if self.parser.should_upgrade() or self.cycle.response_complete:
+        if (
+            self.parser.should_upgrade() and not self.is_http2
+        ) or self.cycle.response_complete:
             return
         self.cycle.more_body = False
         self.cycle.message_event.set()