In a variable valve timing apparatus in which a phase of an intake valve is changed at an amount of change according to a rotational speed of relative rotation between an electric motor as an actuator and a camshaft, the set upper limit value of the rotational speed of relative rotation and a coefficient N.theta. of conversion from a required phase-change amount to the rotational speed of relative rotation .DELTA.Nm in each control period are set at smaller values at the time of engine stop than at the time of engine operation. As a result, the rotational speed of the electric motor in the VVT operation at the time of engine stop is reduced thereby reducing the operation sound of the variable valve timing apparatus.