diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7678ec90081..a3151b1144e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,10 @@
   - The `format` argument changed from optional to required.
   - The returned result changed from a date object to a date-formatted string.
 
+### Bug Fixes
+
+- Fixed a bug that `session.add_packages` can not handle requirement specifier that contains project name with underscore and version.
+
 ## 1.9.0 (2023-10-13)
 
 ### New Features
diff --git a/src/snowflake/snowpark/session.py b/src/snowflake/snowpark/session.py
index 345ac90e133..9c9eb714ad4 100644
--- a/src/snowflake/snowpark/session.py
+++ b/src/snowflake/snowpark/session.py
@@ -8,6 +8,7 @@
 import json
 import logging
 import os
+import re
 import sys
 import tempfile
 from array import array
@@ -1034,10 +1035,18 @@ def _resolve_packages(
             # get the standard package name if there is no underscore
             # underscores are discouraged in package names, but are still used in Anaconda channel
             # pkg_resources.Requirement.parse will convert all underscores to dashes
+            # the regexp is to deal with case that "_" is in the package requirement as well as version restrictions
+            # we only extract the valid package name from the string by following:
+            # https://packaging.python.org/en/latest/specifications/name-normalization/
+            # A valid name consists only of ASCII letters and numbers, period, underscore and hyphen.
+            # It must start and end with a letter or number.
+            # however, we don't validate the pkg name as this is done by pkg_resources.Requirement.parse
+            # find the index of the first char which is not an valid package name character
+            package_name = package_req.key
+            if not use_local_version and "_" in package:
+                reg_match = re.search(r"[^0-9a-zA-Z\-_.]", package)
+                package_name = package[: reg_match.start()] if reg_match else package
 
-            package_name = (
-                package if not use_local_version and "_" in package else package_req.key
-            )
             package_dict[package] = (package_name, use_local_version, package_req)
 
         package_table = "information_schema.packages"
diff --git a/tests/integ/test_packaging.py b/tests/integ/test_packaging.py
index e9e99f0dbcf..819baf3482c 100644
--- a/tests/integ/test_packaging.py
+++ b/tests/integ/test_packaging.py
@@ -283,6 +283,27 @@ def check_if_package_installed() -> bool:
     Utils.check_answer(session.sql(f"select {udf_name}()").collect(), [Row(True)])
 
 
+@pytest.mark.udf
+def test_add_packages_with_underscore_and_versions(session):
+    session.add_packages(["huggingface_hub==0.15.1"])
+    assert session.get_packages() == {
+        "huggingface_hub": "huggingface_hub==0.15.1",
+    }
+    session.clear_packages()
+
+    session.add_packages(["huggingface_hub>0.14.1"])
+    assert session.get_packages() == {
+        "huggingface_hub": "huggingface_hub>0.14.1",
+    }
+    session.clear_packages()
+
+    session.add_packages(["huggingface_hub<=0.15.1"])
+    assert session.get_packages() == {
+        "huggingface_hub": "huggingface_hub<=0.15.1",
+    }
+    session.clear_packages()
+
+
 @pytest.mark.skipif(
     IS_IN_STORED_PROC, reason="Need certain version of datautil/pandas/numpy"
 )