An apparatus controls an internal combustion engine provided with an EGR device having an EGR passage and an EGR valve that is provided in the EGR passage and can adjust an EGR amount. This apparatus includes a controller that estimates state parameters of the internal combustion engine that affect the behavior of the EGR gas within a predetermined period of time; sets constraints on the EGR amount within the predetermined period oh the basis of an approximated dynamics obtained by approximating a true dynamics, which is a transition of the EGR amount within the predetermined period, so that approximated values do not exceed the true dynamics; determines a target value of the EGR amount according to the estimated state parameters within a range of the EGR amount on which the constraints that have been set; and controls the EGR valve so that the EGR amount becomes the determined target value.