The invention is applied to an internal combustion engine in which fuel cut control is performed. The internal combustion engine has an exhaust gas recirculation system including: an exhaust gas recirculation passage that connects an intake and exhaust passage of the engine; and an exhaust gas recirculation valve that changes a cross section of the exhaust gas recirculation passage. A correlation, which holds during a predetermined period of time immediately after fuel cut control is stopped, between engine rotation speed NE and an index value indicating the amount of burned gas contained in the recirculated exhaust gas that passes through the exhaust gas recirculation valve (S101 to S104). The correlation is stored in an electronic control unit in advance (S105). Immediately after the fuel cut control is stopped, the index value indicating the burned gas amount is computed from the correlation stored in the electronic control unit based on the engine rotation speed NE.