diff --git a/CHANGELOG.md b/CHANGELOG.md
index c89049a..febc23e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,6 @@
 ## 2.12.0-wip
-
-- Require Dart 3.4
+* Can decide `runOnce` method of `AsyncMemoizer` will store exception or not.
+* Require Dart 3.4
 
 ## 2.11.0
 
diff --git a/lib/src/async_memoizer.dart b/lib/src/async_memoizer.dart
index c05c927..12588c0 100644
--- a/lib/src/async_memoizer.dart
+++ b/lib/src/async_memoizer.dart
@@ -5,7 +5,9 @@
 import 'dart:async';
 
 /// A class for running an asynchronous function exactly once and caching its
-/// result.
+/// result. If you doesn't want to cache Exception then you can set
+/// [_canCacheException] to false.
+///
 ///
 /// An `AsyncMemoizer` is used when some function may be run multiple times in
 /// order to get its result, but it only actually needs to be run once for its
@@ -27,6 +29,9 @@ import 'dart:async';
 /// }
 /// ```
 class AsyncMemoizer<T> {
+  AsyncMemoizer({bool canCacheException = true}):
+        _canCacheException = canCacheException;
+
   /// The future containing the method's result.
   ///
   /// This can be accessed at any time, and will fire once [runOnce] is called.
@@ -36,11 +41,28 @@ class AsyncMemoizer<T> {
   /// Whether [runOnce] has been called yet.
   bool get hasRun => _completer.isCompleted;
 
+  ///Default is set to true.
+  ///If we set this variable to false.
+  ///On the initial run, if callback returned the [Exception].
+  ///Next time, we can reRun the callback for the successful attempt.
+  final bool _canCacheException;
+
   /// Runs the function, [computation], if it hasn't been run before.
   ///
   /// If [runOnce] has already been called, this returns the original result.
-  Future<T> runOnce(FutureOr<T> Function() computation) {
-    if (!hasRun) _completer.complete(Future.sync(computation));
+  Future<T> runOnce(FutureOr<T> Function() computation) async {
+    if (!hasRun) {
+      if (_canCacheException) {
+        _completer.complete(Future.sync(computation));
+      } else {
+        try {
+          var value = await computation();
+          _completer.complete(value);
+        } catch (error) {
+          rethrow;
+        }
+      }
+    }
     return future;
   }
 }
diff --git a/test/async_memoizer_test.dart b/test/async_memoizer_test.dart
index 490b389..e82c123 100644
--- a/test/async_memoizer_test.dart
+++ b/test/async_memoizer_test.dart
@@ -9,6 +9,14 @@ void main() {
   late AsyncMemoizer cache;
   setUp(() => cache = AsyncMemoizer());
 
+  test('should not store exception when callback throws exception', () async {
+    Future<String> asyncFunctionThatThrows() {
+      throw Exception();
+    }
+    var cacheFuture = cache.runOnce(asyncFunctionThatThrows);
+    await expectLater(cacheFuture,throwsA(isException));
+  });
+
   test('runs the function only the first time runOnce() is called', () async {
     var count = 0;
     expect(await cache.runOnce(() => count++), equals(0));