In an EGR system, a quantity of exhaust gas passing through an EGR valve is computed by an EGR valve model simulating a behavior of the recirculated exhaust gas passing through the EGR valve. An exhaust gas quantity flowing into a cylinder is computed by an EGR-gas-delay model simulating a behavior of the exhaust gas passing through the EGR valve and the throttle valve and then flows into a cylinder. The EGR-gas-delay model includes a confluent-delay model simulating a behavior of EGR gas passing thorough the EGR valve and flowing into the intake passage upstream of the throttle valve; an intake-pipe-delay model simulating a behavior of EGR gas flowing in the intake passage and passing through the throttle valve; and an intake-manifold-delay model simulating a behavior of EGR gas which passes through the throttle valve and then flows into the intake passage downstream of the throttle valve.