A period from ignition timing to maximum heat release rate timing, at which a heat release rate is maximum, within a combustion period of air-fuel mixture is defined as a first combustion period that is one of characteristic values of a heat release rate waveform. The first combustion period is estimated based on a cylinder volume at the maximum heat release rate timing (maximum heat release rate cylinder volume) irrespective of any of an engine load factor, an EGR rate, an air-fuel ratio, an oil or coolant temperature and opening and closing timing of an exhaust valve through correction by the use of the exponential function of an engine rotation speed with an exponent of a value commensurate with a tumble ratio. The heat release rate waveform is calculated by using the estimated first combustion period.