To accurately estimate cylinder intake air quantity when intake air quantity control is performed based on lift of an intake valve.

Effective opening area for each section which is a plurality of divisions of intake valve open period is calculated based on operation angle detection value of the intake valve, intake air quantity for each section is calculated in relation to a parameter based on the effective opening area, cylinder effective stroke volume and engine speed, and integration of the cylinder intake air quantity is calculated as throttle index in relation to the maximum intake air quantity at a time of full open operation.