By means of an air model, an estimated quantity of an exhaust gas flowing into a cylinder and a target quantity of the exhaust gas are computed. A deviation between the estimated quantity and the target quantity is multiplied by a feedback gain to obtain a feedback correction quantity. A reference opening degree of an EGR valve is defined according to an engine driving condition and the feedback correction quantity is added to the reference opening degree to obtain a command opening degree of the EGR valve. According to the engine driving condition and the deviation between the estimated quantity and the target quantity, a feedback gain is established so that control accuracy and control stability of a feedback control can be ensured.