A method of controlling a damper pulley clutch for selectively transmitting power of an engine to engine accessories, may include determining, by a controller, whether a vehicle is driven in a fuel-cut mode under deceleration of the vehicle and controlling the damper pulley clutch, by the controller, to be engaged upon determining that the vehicle is driven in the fuel-cut mode and to be disengaged upon determining that the vehicle is not driven in the fuel-cut mode.