A controller for controlling a valve timing of an engine that calculates a duty correction value using an arithmetic expression reflecting a physical model, which is associated with torque applied to an exhaust valve camshaft, a spring force exerted by an advancing spring for varying a rotational phase of the exhaust valve camshaft, and hydraulic pressure of operating oil. When the coolant temperature is lower than 80° C., the controller sets the duty correction value to zero. The duty correction value reflecting all the fluctuation factors of the engine is easily obtained without using a map requiring a large amount of data.