A time-course change (dM/dt) in the mass of air in an intake passage downstream of a throttle value is estimated through application of a mass conservation law to the air in the passage. A time-course change dTm/dt in the temperature of the air in the passage is estimated through application of an energy conservation law to the air in the passage. The pressure of the air in the passage is estimated on the basis of the mass of the air in the passage obtained through integration of dM/dt with respect to time, the intake air temperature obtained through integration of dTm/dt with respect to time, and a state equation applied to the air in the passage. Only the state equation includes a term regarding the volume of the passage. Therefore, it is possible to easily identify the volume while monitoring only a change in the intake air pressure.