An electronic control unit detects an index value of an amount of generated heat of fuel to be combusted in a diesel engine. The electronic control unit also executes the injection of a predetermined amount of the fuel to estimate a cetane number of the fuel and calculates an index value of output torque of the diesel engine generated with that execution. Then, the electronic control unit calculates an estimated value of the cetane number of the fuel based on the index value of the output torque and the index value of the amount of generated heat.