This air quantity estimation apparatus inputs an output quantity Vafm of an air flowmeter 61 disposed in an intake passage upstream of a compressor 91a to an AFM inverse model M1 to thereby estimate the flow rate (compressor-inflow-air flow rate) mcmi of air actually flowing into the compressor, which flow rate has been compensated for detection delay. This apparatus estimates the quantity of air introduced in a cylinder (cylinder-interior air quantity) Klfwd at a future time point after the present time point on the basis of the estimated actual compressor-inflow-air flow rate mcmi employed as a flow rate of air actually flowing out of the compressor at the present time point, and first and second air models M10 and M20 which describe the behavior of air within the intake passage downstream of the compressor in accordance with physical laws.