An EGR system includes a high-pressure EGR unit and a low-pressure EGR unit. During the steady operation of an internal combustion engine, the high-pressure EGR gas and the low-pressure EGR gas are mixed with each other at a mixture ratio, in which the ratio of the high-pressure EGR gas amount to the entire EGR gas amount is higher than that in a known mixture ratio, and then recirculated back to the internal combustion engine. In the engine speed-up transitional operation period, the opening amount of a high-pressure EGR valve is adjusted to the opening amount that is much smaller than the target opening amount corresponding to the target operation mode. Thus, it is possible to suppress occurrence of the situation where the entire EGR gas amount is excessive in the period in which the low-pressure EGR gas amount does not decrease by a sufficient amount.