diff --git a/CHANGES.rst b/CHANGES.rst
index 8b415ef..b75db4d 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -8,6 +8,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 - Added special monkeypatching if `Apport <https://github.com/canonical/apport>`_ has
   overridden ``sys.excepthook`` so it will format exception groups correctly
   (PR by John Litborn)
+- Added a backport of ``contextlib.suppress()`` from Python 3.12.1 which also handles
+  suppressing exceptions inside exception groups
 - Fixed bare ``raise`` in a handler reraising the original naked exception rather than
   an exception group which is what is raised when you do a ``raise`` in an ``except*``
   handler
diff --git a/README.rst b/README.rst
index 48178d9..d5203fd 100644
--- a/README.rst
+++ b/README.rst
@@ -26,6 +26,8 @@ It contains the following:
   * ``traceback.format_exception_only()``
   * ``traceback.print_exception()``
   * ``traceback.print_exc()``
+* A backported version of ``contextlib.suppress()`` from Python 3.12.1 which also
+  handles suppressing exceptions inside exception groups
 
 If this package is imported on Python 3.11 or later, the built-in implementations of the
 exception group classes are used instead, ``TracebackException`` is not monkey patched
@@ -84,6 +86,18 @@ would be written with this backport like this:
 **NOTE**: Just like with ``except*``, you cannot handle ``BaseExceptionGroup`` or
 ``ExceptionGroup`` with ``catch()``.
 
+Suppressing exceptions
+======================
+
+This library contains a backport of the ``contextlib.suppress()`` context manager from
+Python 3.12.1. It allows you to selectively ignore certain exceptions, even when they're
+inside exception groups::
+
+    from exceptiongroup import suppress
+
+    with suppress(RuntimeError):
+        raise ExceptionGroup("", [RuntimeError("boo")])
+
 Notes on monkey patching
 ========================
 
diff --git a/src/exceptiongroup/__init__.py b/src/exceptiongroup/__init__.py
index 0e7e02b..d8e36b2 100644
--- a/src/exceptiongroup/__init__.py
+++ b/src/exceptiongroup/__init__.py
@@ -6,6 +6,7 @@
     "format_exception_only",
     "print_exception",
     "print_exc",
+    "suppress",
 ]
 
 import os
@@ -38,3 +39,8 @@
 
     BaseExceptionGroup = BaseExceptionGroup
     ExceptionGroup = ExceptionGroup
+
+if sys.version_info < (3, 12, 1):
+    from ._suppress import suppress
+else:
+    from contextlib import suppress
diff --git a/src/exceptiongroup/_suppress.py b/src/exceptiongroup/_suppress.py
new file mode 100644
index 0000000..6741563
--- /dev/null
+++ b/src/exceptiongroup/_suppress.py
@@ -0,0 +1,40 @@
+import sys
+from contextlib import AbstractContextManager
+
+if sys.version_info < (3, 11):
+    from ._exceptions import BaseExceptionGroup
+
+
+class suppress(AbstractContextManager):
+    """Backport of :class:`contextlib.suppress` from Python 3.12.1."""
+
+    def __init__(self, *exceptions):
+        self._exceptions = exceptions
+
+    def __enter__(self):
+        pass
+
+    def __exit__(self, exctype, excinst, exctb):
+        # Unlike isinstance and issubclass, CPython exception handling
+        # currently only looks at the concrete type hierarchy (ignoring
+        # the instance and subclass checking hooks). While Guido considers
+        # that a bug rather than a feature, it's a fairly hard one to fix
+        # due to various internal implementation details. suppress provides
+        # the simpler issubclass based semantics, rather than trying to
+        # exactly reproduce the limitations of the CPython interpreter.
+        #
+        # See http://bugs.python.org/issue12029 for more details
+        if exctype is None:
+            return
+
+        if issubclass(exctype, self._exceptions):
+            return True
+
+        if issubclass(exctype, BaseExceptionGroup):
+            match, rest = excinst.split(self._exceptions)
+            if rest is None:
+                return True
+
+            raise rest
+
+        return False
diff --git a/tests/test_suppress.py b/tests/test_suppress.py
new file mode 100644
index 0000000..289bb33
--- /dev/null
+++ b/tests/test_suppress.py
@@ -0,0 +1,16 @@
+import sys
+
+import pytest
+
+from exceptiongroup import suppress
+
+if sys.version_info < (3, 11):
+    from exceptiongroup import BaseExceptionGroup, ExceptionGroup
+
+
+def test_suppress_exception():
+    with pytest.raises(ExceptionGroup) as exc, suppress(SystemExit):
+        raise BaseExceptionGroup("", [SystemExit(1), RuntimeError("boo")])
+
+    assert len(exc.value.exceptions) == 1
+    assert isinstance(exc.value.exceptions[0], RuntimeError)