A valve overlap period is increased as a desired torque of an engine increases by advancing an opening timing of an intake valve at a rate greater than that of retarding a closing timing of an exhaust valve in a low engine-torque area in which the desired torque of the internal combustion engine is relatively low (step S16). The valve overlap period is increased as the desired torque of the engine increases by retarding the closing timing of the exhaust valve at a rate greater than that of advancing the opening timing of the intake valve in a high engine-torque area in which the desired torque of the internal combustion engine is relatively high (step S17). Accordingly, the drivability can be improved by obtaining the proper torque and the smooth torque curve in the wide driving area.