An engine includes: a duration apparatus for adjusting an opening duration of an intake valve, a Cylinder De-Activation (CDA) apparatus for controlling deactivation of an exhaust valve, an igniter, an injector for injecting a fuel, an operation state signal unit for measuring an operation state of a vehicle, and a controller for controlling the operations of the duration apparatus, the CDA apparatus, the igniter, and the injector based on an output signal from the operation state signal unit. A control method for this engine includes: determining, by the controller, whether the operation state of the vehicle corresponds to a CDA operation mode; and when the CDA operation mode is determined, operating the CDA apparatus so as to stop the operations of the igniter and the injector, increase an opening duration of the intake valve, and deactivate the exhaust valve by controlling the CDA apparatus.