diff --git a/lib/deploy/stepFunctions/compileIamRole.js b/lib/deploy/stepFunctions/compileIamRole.js
index a6659e46..02cf6efd 100644
--- a/lib/deploy/stepFunctions/compileIamRole.js
+++ b/lib/deploy/stepFunctions/compileIamRole.js
@@ -225,6 +225,13 @@ function getLambdaPermissions(state) {
     }];
   }
 
+  if (state.Parameters['FunctionName.$']) {
+    return [{
+      action: 'lambda:InvokeFunction',
+      resource: state.Parameters.AllowedFunctions ? state.Parameters.AllowedFunctions : '*',
+    }];
+  }
+
   // hope for the best...
   return [{
     action: 'lambda:InvokeFunction',
diff --git a/lib/deploy/stepFunctions/compileIamRole.test.js b/lib/deploy/stepFunctions/compileIamRole.test.js
index 61cfc8d7..de9f8f47 100644
--- a/lib/deploy/stepFunctions/compileIamRole.test.js
+++ b/lib/deploy/stepFunctions/compileIamRole.test.js
@@ -1831,4 +1831,101 @@ describe('#compileIamRole', () => {
       'logs:DescribeLogGroups',
     ]);
   });
+
+  it('should support variable FunctionName', () => {
+    serverless.service.stepFunctions = {
+      stateMachines: {
+        myStateMachine1: {
+          id: 'StateMachine1',
+          definition: {
+            StartAt: 'A',
+            States: {
+              A: {
+                Type: 'Task',
+                Resource: 'arn:aws:states:::lambda:invoke.waitForTaskToken',
+                Parameters: {
+                  'FunctionName.$': '$.functionName',
+                  Payload: {
+                    'model.$': '$.new_model',
+                    'token.$': '$$.Task.Token',
+                  },
+                },
+                Next: 'B',
+              },
+              B: {
+                Type: 'Task',
+                Resource: 'arn:aws:states:::lambda:invoke.waitForTaskToken',
+                Parameters: {
+                  'FunctionName.$': '$.functionName',
+                  AllowedFunctions: '*limited*',
+                  Payload: {
+                    'model.$': '$.new_model',
+                    'token.$': '$$.Task.Token',
+                  },
+                },
+                End: true,
+              },
+            },
+          },
+        },
+      },
+    };
+    serverlessStepFunctions.compileIamRole();
+    const statements = serverlessStepFunctions.serverless.service
+      .provider.compiledCloudFormationTemplate.Resources.StateMachine1Role
+      .Properties.Policies[0].PolicyDocument.Statement;
+    const lambdaPermissions = statements.filter(s => _.isEqual(s.Action, ['lambda:InvokeFunction']));
+    expect(lambdaPermissions).to.have.lengthOf(1);
+    expect(lambdaPermissions[0].Resource).to.deep.equal('*');
+    // Run the test again with limitations added
+    serverless.service.stepFunctions = {
+      stateMachines: {
+        myStateMachine1: {
+          id: 'StateMachine1',
+          definition: {
+            StartAt: 'A',
+            States: {
+              A: {
+                Type: 'Task',
+                Resource: 'arn:aws:states:::lambda:invoke.waitForTaskToken',
+                Parameters: {
+                  'FunctionName.$': '$.functionName',
+                  AllowedFunctions: 'arn:aws:lambda:us-west-2:1234567890:function:foo',
+                  Payload: {
+                    'model.$': '$.new_model',
+                    'token.$': '$$.Task.Token',
+                  },
+                },
+                Next: 'B',
+              },
+              B: {
+                Type: 'Task',
+                Resource: 'arn:aws:states:::lambda:invoke.waitForTaskToken',
+                Parameters: {
+                  'FunctionName.$': '$.functionName',
+                  AllowedFunctions: '*limited*',
+                  Payload: {
+                    'model.$': '$.new_model',
+                    'token.$': '$$.Task.Token',
+                  },
+                },
+                End: true,
+              },
+            },
+          },
+        },
+      },
+    };
+    serverlessStepFunctions.compileIamRole();
+    const statements2 = serverlessStepFunctions.serverless.service
+      .provider.compiledCloudFormationTemplate.Resources.StateMachine1Role
+      .Properties.Policies[0].PolicyDocument.Statement;
+    const lambdaPermissions2 = statements2.filter(s => _.isEqual(s.Action, ['lambda:InvokeFunction']));
+    expect(lambdaPermissions2).to.have.lengthOf(1);
+    console.log(lambdaPermissions2);
+    expect(lambdaPermissions2[0].Resource).to.deep.equal([
+      'arn:aws:lambda:us-west-2:1234567890:function:foo',
+      '*limited*',
+    ]);
+  });
 });