diff --git a/langchain/document_loaders/web_base.py b/langchain/document_loaders/web_base.py
index 1528cd6156..1d4f0aee23 100644
--- a/langchain/document_loaders/web_base.py
+++ b/langchain/document_loaders/web_base.py
@@ -60,7 +60,7 @@ class WebBaseLoader(BaseLoader):
         self,
         web_path: Union[str, List[str]],
         header_template: Optional[dict] = None,
-        verify: Optional[bool] = True,
+        verify_ssl: Optional[bool] = True,
         proxies: Optional[dict] = None,
     ):
         """Initialize with webpage path."""
@@ -73,7 +73,6 @@ class WebBaseLoader(BaseLoader):
         elif isinstance(web_path, List):
             self.web_paths = web_path
 
-        self.session = requests.Session()
         try:
             import bs4  # noqa:F401
         except ImportError:
@@ -81,9 +80,6 @@ class WebBaseLoader(BaseLoader):
                 "bs4 package not found, please install it with " "`pip install bs4`"
             )
 
-        # Choose to verify
-        self.verify = verify
-
         headers = header_template or default_header_template
         if not headers.get("User-Agent"):
             try:
@@ -96,7 +92,10 @@ class WebBaseLoader(BaseLoader):
                     "To get a realistic header for requests, "
                     "`pip install fake_useragent`."
                 )
+
+        self.session = requests.Session()
         self.session.headers = dict(headers)
+        self.session.verify = verify_ssl
 
         if proxies:
             self.session.proxies.update(proxies)
@@ -110,17 +109,13 @@ class WebBaseLoader(BaseLoader):
     async def _fetch(
         self, url: str, retries: int = 3, cooldown: int = 2, backoff: float = 1.5
     ) -> str:
-        # For SiteMap SSL verification
-        if not self.requests_kwargs.get("verify", True):
-            connector = aiohttp.TCPConnector(ssl=False)
-        else:
-            connector = None
-
-        async with aiohttp.ClientSession(connector=connector) as session:
+        async with aiohttp.ClientSession() as session:
             for i in range(retries):
                 try:
                     async with session.get(
-                        url, headers=self.session.headers, verify=self.verify
+                        url,
+                        headers=self.session.headers,
+                        ssl=None if self.session.verify else False,
                     ) as response:
                         return await response.text()
                 except aiohttp.ClientConnectionError as e:
@@ -195,7 +190,7 @@ class WebBaseLoader(BaseLoader):
 
         self._check_parser(parser)
 
-        html_doc = self.session.get(url, verify=self.verify, **self.requests_kwargs)
+        html_doc = self.session.get(url, **self.requests_kwargs)
         if self.raise_for_status:
             html_doc.raise_for_status()
         html_doc.encoding = html_doc.apparent_encoding