diff --git a/changelogs/fragments/pip-fix-idempotence-in-check-mode.yaml b/changelogs/fragments/pip-fix-idempotence-in-check-mode.yaml
new file mode 100644
index 00000000000..f3cc2ffd0a3
--- /dev/null
+++ b/changelogs/fragments/pip-fix-idempotence-in-check-mode.yaml
@@ -0,0 +1,2 @@
+bugfixes:
+- "pip - idempotence in check mode now works correctly."
diff --git a/lib/ansible/modules/packaging/language/pip.py b/lib/ansible/modules/packaging/language/pip.py
index 8683a407545..9b39cd3fd33 100644
--- a/lib/ansible/modules/packaging/language/pip.py
+++ b/lib/ansible/modules/packaging/language/pip.py
@@ -350,10 +350,11 @@ def _is_present(module, req, installed_pkgs, pkg_command):
     for pkg in installed_pkgs:
         if '==' in pkg:
             pkg_name, pkg_version = pkg.split('==')
+            pkg_name = Package.canonicalize_name(pkg_name)
         else:
             continue
 
-        if pkg_name.lower() == req.package_name and req.is_satisfied_by(pkg_version):
+        if pkg_name == req.package_name and req.is_satisfied_by(pkg_version):
             return True
 
     return False
@@ -499,6 +500,8 @@ class Package:
     test whether a package is already satisfied.
     """
 
+    _CANONICALIZE_RE = re.compile(r'[-_.]+')
+
     def __init__(self, name_string, version_string=None):
         self._plain_package = False
         self.package_name = name_string
@@ -515,7 +518,7 @@ class Package:
                 self.package_name = "setuptools"
                 self._requirement.project_name = "setuptools"
             else:
-                self.package_name = self._requirement.project_name
+                self.package_name = Package.canonicalize_name(self._requirement.project_name)
             self._plain_package = True
         except ValueError as e:
             pass
@@ -539,6 +542,11 @@ class Package:
                 for op, ver in self._requirement.specs
             )
 
+    @staticmethod
+    def canonicalize_name(name):
+        # This is taken from PEP 503.
+        return Package._CANONICALIZE_RE.sub("-", name).lower()
+
     def __str__(self):
         if self._plain_package:
             return to_native(self._requirement)
diff --git a/test/integration/targets/pip/tasks/pip.yml b/test/integration/targets/pip/tasks/pip.yml
index dd84724f262..b7036de99de 100644
--- a/test/integration/targets/pip/tasks/pip.yml
+++ b/test/integration/targets/pip/tasks/pip.yml
@@ -213,6 +213,27 @@
     that:
       - "not (q_check_mode is changed)"
 
+# Case with package name that has a different package name case and an
+# underscore instead of a hyphen
+- name: check for Junit-XML package
+  pip:
+    name: Junit-XML
+    virtualenv: "{{ output_dir }}/pipenv"
+    state: present
+
+- name: check for Junit-XML package in check_mode
+  pip:
+    name: Junit-XML
+    virtualenv: "{{ output_dir }}/pipenv"
+    state: present
+  check_mode: True
+  register: diff_case_check_mode
+
+- name: make sure Junit-XML in check_mode doesn't report changed
+  assert:
+    that:
+      - "diff_case_check_mode is not changed"
+
 # ansible#23204
 - name: ensure is a fresh virtualenv
   file: