A method for controlling intake and exhaust valves of an engine includes: controlling, by an intake continuous variable valve timing (CVVT) device, opening and closing timings of the intake valve; controlling, by an exhaust CVVT device, opening and closing timing of the exhaust valve; determining, by a controller, first to fifth control regions based on engine load and speeds, and a target opening duration of the intake valve and target opening or target closing timings of the intake valve; modifying, by an intake continuous variable valve duration (CVVD) device, current opening and closing timings of the intake valve based on the target opening duration; and advancing or retarding, by the intake CVVD device, the current opening timing of the intake valve while simultaneously retarding or advancing the current closing timing of the intake valve by a predetermined value based on the target opening duration of the intake valve.