A heat generation rate waveform of an internal combustion engine. A period from spark generated by an ignition plug to ignition of an air-fuel mixture is defined as an ignition delay period τ that is one of characteristic values of the heat generation rate waveform. When the ignition time FA of the air-fuel mixture is on the advance side of a compression top dead center of a piston (BTDC), the ignition delay period τ is estimated based on an in-cylinder fuel density ρfuel@SA at the spark time SA, and when the ignition time FA of the air-fuel mixture is on the delay side of the compression top dead center of the piston (ATDC), the ignition delay period τ is estimated based on an in-cylinder fuel density ρfuel@FA at the ignition time FA. Thus, the heat generation rate waveform is produced using the estimated ignition delay period τ.