Respective learned values of four parameters, that are an intake valve working angle deviation amount, an exhaust valve working angle deviation amount, an intake valve timing deviation amount and an exhaust pressure loss deviation amount, are calculated based on learned values of an intake valve flow rate error that are obtained under at least four different operating conditions. A correction amount with respect to an intake valve flow rate that is calculated with an intake valve model equation is calculated based on respective learned values of the four parameters using an intake valve flow rate error model equation in which coefficients are represented by functions of state quantities of an engine that include an engine speed and an intake pipe pressure.