A device for purifying the exhaust gas of an internal combustion engine is disclosed. The device comprises a particulate trap disposed in the engine exhaust system, an exhaust gas recirculation passage communicating the upstream of the particulate trap in the engine exhaust system with the engine intake system, a control valve for controlling the amount of exhaust gas recirculated through the exhaust gas recirculation passage to be an optimum amount in accordance with an engine operating condition. In the device, an amount of the fresh air introduced into the engine intake system during a fuel-cut is detected, and an amount of particulate trapped by the particulate trap is estimated on the basis of the amount of fresh air detected after the control valve is opened to a predetermined opening degree.