diff --git a/packages/@aws-cdk/custom-resources/README.md b/packages/@aws-cdk/custom-resources/README.md
index 13cd4a4002fe3..e75d619a7875e 100644
--- a/packages/@aws-cdk/custom-resources/README.md
+++ b/packages/@aws-cdk/custom-resources/README.md
@@ -380,6 +380,19 @@ Since a successful resource provisioning might or might not produce outputs, thi
 
 In both the cases, you will get a synth time error if you attempt to use it in conjunction with `ignoreErrorCodesMatching`.
 
+### Customizing the Lambda function implementing the custom resource
+Use the `role`, `timeout` and `logRetention` properties to customize the Lambda function implementing the custom
+resource:
+
+```ts
+new AwsCustomResource(this, 'Customized', {
+  // other props here
+  role: myRole, // must be assumable by the `lambda.amazonaws.com` service principal
+  timeout: cdk.Duration.minutes(10) // defaults to 2 minutes
+  logRetention: logs.RetentionDays.ONE_WEEK // defaults to never delete logs
+})
+```
+
 ### Examples
 
 #### Verify a domain with SES
diff --git a/packages/@aws-cdk/custom-resources/lib/aws-custom-resource/aws-custom-resource.ts b/packages/@aws-cdk/custom-resources/lib/aws-custom-resource/aws-custom-resource.ts
index 881954c056e97..e0ea2b0d06199 100644
--- a/packages/@aws-cdk/custom-resources/lib/aws-custom-resource/aws-custom-resource.ts
+++ b/packages/@aws-cdk/custom-resources/lib/aws-custom-resource/aws-custom-resource.ts
@@ -1,6 +1,7 @@
 import { CustomResource, CustomResourceProvider } from '@aws-cdk/aws-cloudformation';
 import * as iam from '@aws-cdk/aws-iam';
 import * as lambda from '@aws-cdk/aws-lambda';
+import * as logs from '@aws-cdk/aws-logs';
 import * as cdk from '@aws-cdk/core';
 import * as fs from 'fs';
 import * as path from 'path';
@@ -235,6 +236,14 @@ export interface AwsCustomResourceProps {
    * @default Duration.minutes(2)
    */
   readonly timeout?: cdk.Duration
+
+  /**
+   * The number of days log events of the Lambda function implementing
+   * this custom resource are kept in CloudWatch Logs.
+   *
+   * @default logs.RetentionDays.INFINITE
+   */
+  readonly logRetention?: logs.RetentionDays;
 }
 
 /**
@@ -292,6 +301,7 @@ export class AwsCustomResource extends cdk.Construct implements iam.IGrantable {
       lambdaPurpose: 'AWS',
       timeout: props.timeout || cdk.Duration.minutes(2),
       role: props.role,
+      logRetention: props.logRetention,
     });
     this.grantPrincipal = provider.grantPrincipal;
 
diff --git a/packages/@aws-cdk/custom-resources/package.json b/packages/@aws-cdk/custom-resources/package.json
index 38264cb2ad94a..b5c1ee73f71c9 100644
--- a/packages/@aws-cdk/custom-resources/package.json
+++ b/packages/@aws-cdk/custom-resources/package.json
@@ -87,6 +87,7 @@
     "@aws-cdk/aws-cloudformation": "0.0.0",
     "@aws-cdk/aws-iam": "0.0.0",
     "@aws-cdk/aws-lambda": "0.0.0",
+    "@aws-cdk/aws-logs": "0.0.0",
     "@aws-cdk/aws-sns": "0.0.0",
     "@aws-cdk/aws-stepfunctions": "0.0.0",
     "@aws-cdk/aws-stepfunctions-tasks": "0.0.0",
@@ -97,6 +98,7 @@
     "@aws-cdk/aws-cloudformation": "0.0.0",
     "@aws-cdk/aws-iam": "0.0.0",
     "@aws-cdk/aws-lambda": "0.0.0",
+    "@aws-cdk/aws-logs": "0.0.0",
     "@aws-cdk/aws-sns": "0.0.0",
     "@aws-cdk/aws-stepfunctions": "0.0.0",
     "@aws-cdk/aws-stepfunctions-tasks": "0.0.0",
diff --git a/packages/@aws-cdk/custom-resources/test/aws-custom-resource/aws-custom-resource.test.ts b/packages/@aws-cdk/custom-resources/test/aws-custom-resource/aws-custom-resource.test.ts
index 27e3b89311703..4f5dcc5ec34d0 100644
--- a/packages/@aws-cdk/custom-resources/test/aws-custom-resource/aws-custom-resource.test.ts
+++ b/packages/@aws-cdk/custom-resources/test/aws-custom-resource/aws-custom-resource.test.ts
@@ -1,5 +1,6 @@
 import '@aws-cdk/assert/jest';
 import * as iam from '@aws-cdk/aws-iam';
+import * as logs from '@aws-cdk/aws-logs';
 import * as cdk from '@aws-cdk/core';
 import { AwsCustomResource, AwsCustomResourcePolicy, PhysicalResourceId } from '../../lib';
 
@@ -488,3 +489,35 @@ test('getDataString', () => {
     }
   });
 });
+
+test('can specify log retention', () => {
+  // GIVEN
+  const stack = new cdk.Stack();
+
+  // WHEN
+  new AwsCustomResource(stack, 'AwsSdk', {
+    onCreate: {
+      service: 'service',
+      action: 'action',
+      physicalResourceId: PhysicalResourceId.of('id')
+    },
+    logRetention: logs.RetentionDays.ONE_WEEK,
+    policy: AwsCustomResourcePolicy.fromSdkCalls({ resources: AwsCustomResourcePolicy.ANY_RESOURCE })
+  });
+
+  // THEN
+  expect(stack).toHaveResource('Custom::LogRetention', {
+    LogGroupName: {
+      'Fn::Join': [
+        '',
+        [
+          '/aws/lambda/',
+          {
+            Ref: 'AWS679f53fac002430cb0da5b7982bd22872D164C4C'
+          }
+        ]
+      ]
+    },
+    RetentionInDays: 7
+  });
+});