An engine that re-circulates its exhaust gas suffers decreased accuracy in estimating an EGR rate real-time especially while the operating state of the engine is in a transitional state, which often results in torque fluctuations and deteriorated exhaust gas.A sensor for directly detecting an EGR flow rate is disposed in an EGR path. An EGR rate and in-cylinder oxygen concentration are calculated from the output value of that sensor. In addition, when this EGR rate calculation method is used, the calculation is properly switched between a steady operation state characterized by a low load and small rotational fluctuations and a transitional operating state including the acceleration and deceleration. This makes it possible to correctly estimate the EGR rate and the in-cylinder oxygen concentration under a wide range of engine operation conditions, and thereby to avoid the fluctuation of torque and the deterioration of exhaust gas.