An electronic control unit calculates a rotation variation amount ΣΔNE as a cetane number index value of the fuel supplied to an internal combustion engine and executes fuel injection control in a first execution mode corresponding to the rotation variation amount ΣΔNE (S407, S408). In a mixing period in which the cetane number of the fuel supplied to the internal combustion engine is changed due to the fuel feed into the fuel tank (S401: YES), the fuel injection control is executed in a second execution mode such that, compared with the first execution mode, stable operation of the internal combustion engine is given more importance (S402:YES, S403). When calculation of the rotation variation amount ΣΔNE is executed during the mixing period (S404: YES), fuel injection control is executed while limiting the reflection of the rotation variation amount ΣΔNE (S405, S406).