diff --git a/packages/@aws-cdk/aws-stepfunctions/lib/states/state.ts b/packages/@aws-cdk/aws-stepfunctions/lib/states/state.ts
index dfc9f8f75c246..e99559edaab43 100644
--- a/packages/@aws-cdk/aws-stepfunctions/lib/states/state.ts
+++ b/packages/@aws-cdk/aws-stepfunctions/lib/states/state.ts
@@ -24,6 +24,16 @@ export interface StateProps {
      */
     inputPath?: string;
 
+    /**
+     * Parameters pass a collection of key-value pairs, either static values or JSONPath expressions that select from the input.
+     *
+     * @see
+     * https://docs.aws.amazon.com/step-functions/latest/dg/input-output-inputpath-params.html#input-output-parameters
+     *
+     * @default No parameters
+     */
+    parameters?: { [name: string]: any };
+
     /**
      * JSONPath expression to select part of the state to be the output to this state.
      *
@@ -112,6 +122,7 @@ export abstract class State extends cdk.Construct implements IChainable {
     // pragmatic!
     protected readonly comment?: string;
     protected readonly inputPath?: string;
+    protected readonly parameters?: object;
     protected readonly outputPath?: string;
     protected readonly resultPath?: string;
     protected readonly branches: StateGraph[] = [];
@@ -144,6 +155,7 @@ export abstract class State extends cdk.Construct implements IChainable {
 
         this.comment = props.comment;
         this.inputPath = props.inputPath;
+        this.parameters = props.parameters;
         this.outputPath = props.outputPath;
         this.resultPath = props.resultPath;
     }
@@ -297,11 +309,12 @@ export abstract class State extends cdk.Construct implements IChainable {
     }
 
     /**
-     * Render InputPath/OutputPath in ASL JSON format
+     * Render InputPath/Parameters/OutputPath in ASL JSON format
      */
     protected renderInputOutput(): any {
         return {
             InputPath: renderJsonPath(this.inputPath),
+            Parameters: this.parameters,
             OutputPath: renderJsonPath(this.outputPath),
         };
     }
diff --git a/packages/@aws-cdk/aws-stepfunctions/lib/states/task.ts b/packages/@aws-cdk/aws-stepfunctions/lib/states/task.ts
index b540dacf30787..a6ed6025de560 100644
--- a/packages/@aws-cdk/aws-stepfunctions/lib/states/task.ts
+++ b/packages/@aws-cdk/aws-stepfunctions/lib/states/task.ts
@@ -34,6 +34,16 @@ export interface TaskProps {
      */
     inputPath?: string;
 
+    /**
+     * Parameters pass a collection of key-value pairs, either static values or JSONPath expressions that select from the input.
+     *
+     * @see
+     * https://docs.aws.amazon.com/step-functions/latest/dg/input-output-inputpath-params.html#input-output-parameters
+     *
+     * @default No parameters
+     */
+    parameters?: { [name: string]: any };
+
     /**
      * JSONPath expression to select part of the state to be the output to this state.
      *
diff --git a/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine-resources.ts b/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine-resources.ts
index 6484828c19ec9..b3adf4581b955 100644
--- a/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine-resources.ts
+++ b/packages/@aws-cdk/aws-stepfunctions/test/test.state-machine-resources.ts
@@ -91,6 +91,48 @@ export = {
             statistic: 'Sum'
         });
 
+        test.done();
+    },
+
+    'Task should render InputPath / Parameters / OutputPath correctly'(test: Test) {
+        // GIVEN
+        const stack = new cdk.Stack();
+        const task = new stepfunctions.Task(stack, 'Task', {
+            resource: new FakeResource(),
+            inputPath: "$",
+            outputPath: "$.state",
+            parameters: {
+                "input.$": "$",
+                "stringArgument": "inital-task",
+                "numberArgument": 123,
+                "booleanArgument": true,
+                "arrayArgument": ["a", "b", "c"]
+            }
+        });
+
+        // WHEN
+        const taskState = task.toStateJson();
+
+        // THEN
+        test.deepEqual(taskState, { End: true,
+            Retry: undefined,
+            Catch: undefined,
+            InputPath: '$',
+            Parameters:
+             { 'input.$': '$',
+               'stringArgument': 'inital-task',
+               'numberArgument': 123,
+               'booleanArgument': true,
+               'arrayArgument': [ 'a', 'b', 'c' ] },
+            OutputPath: '$.state',
+            Type: 'Task',
+            Comment: undefined,
+            Resource: 'resource',
+            ResultPath: undefined,
+            TimeoutSeconds: undefined,
+            HeartbeatSeconds: undefined
+        });
+
         test.done();
     }
 };