The objective of the present invention is to control the valve timing (VT) appropriately when multiple minimum points or maximum points exist in a characteristic line representing the relationship between the valve timing and the amount of air. An engine (10) is equipped with variable valve timing systems (42, 44) and the like. First, when a prescribed driving condition is satisfied, wherein multiple maximum points exist in a load characteristic line representing the relationship between the valve timing for an intake valve (32) and a load KL, an ECU (60) calculates the valve timing corresponding to the maximum value KLmax of the load KL as the maximum air amount VT (VTmax). When the maximum value KLmax of the load KL is smaller than a target KL, the VT is changed toward VTmax. Thus, the direction in which the valve timing is changed is determined on the basis of VTmax, which is calculated irrespective of the current change tendency (gradient) of the characteristic line or the like. Accordingly, it is possible to prevent the valve timing from being influenced by the gradient of the characteristic line or the like and latching onto a maximum point which is not the optimal point, even when multiple maximum points exist in the characteristic line for indicating the air amount.