An EGR apparatus includes a EGR passage and an EGR valve provided in the EGR passage to regulate an EGR flow rate in the EGR passage. An ECU closes the EGR valve from an open state prior to start of deceleration of the engine based on engine rotation speed detected by a rotation speed sensor, accelerator opening degree detected by an accelerator sensor, and actual opening degree of the EGR valve. During deceleration of the engine, the ECU obtains a target opening degree of the EGR valve according to the separately detected engine rotation speed and accelerator opening degree from a target opening degree map and starts to close the EGR valve when a difference between an actual opening degree and the target opening degree of the EGR valve exceeds a predetermined value.