A reference model simulates a desired response characteristic of the variable valve timing apparatus and is constructed by using a dynamic characteristic in a region of the maximum changing speed of the valve timing of the variable valve timing apparatus. The variable valve timing apparatus is constructed of the control system with two degrees of freedom in which in the controller, the feedback duty is calculated so that the deviation between the output obtained by applying the time delay to the output of the quickest response model and the valve timing is small, and in the reverse VCT model, the feed forward duty is calculated so that the target advance amount is realized based upon the output of the quickest response model, and the control duty of the variable valve timing apparatus is obtained by addition of the feedback duty and the feed forward duty.