A control method for an engine includes determining whether a predetermined fuel supply stop condition has been fulfilled, executing stop time vibration suppression control of, after stop of fuel supply in response to fulfillment of the predetermined fuel supply stop condition, temporarily performing fuel supply to the engine to suppress vehicle vibration, and stopping fuel supply to all cylinders after the execution of the stop time vibration suppression control. The stop time vibration suppression control includes determining whether a first predetermined number of cylinders have undergone a combustion stroke after the stop of the fuel supply, the first predetermined number being according to a engine revolution speed or a reduction ratio from the engine to drive wheels, and in a case where the first predetermined number of cylinders have undergone the combustion stroke, performing fuel supply to a second predetermined number of cylinders.