An air quantity estimation apparatus for an internal combustion engine including an intake passage for introducing air taken from the outside of the engine into a cylinder; a supercharger disposed in the intake passage and including a compressor for compressing air within the intake passage; a throttle valve disposed in the intake passage to be located downstream of the supercharger, the opening of the throttle valve being adjustable for changing the quantity of air passing through the intake passage; and an intake valve disposed downstream of the throttle valve and driven to make a connection portion between the intake passage and the cylinder into a communicating state or a blocked state, the air quantity estimation apparatus estimating cylinder air quantity, which is a quantity of air introduced into the cylinder, on the basis of a physical model representing the behavior of air passing through the intake passage, the air quantity estimation apparatus characterized by comprising: first pressure estimation means for estimating throttle valve upstream pressure as pressure of air within a throttle valve upstream section, which is a portion of the intake passage between the supercharger and the throttle valve, and estimating throttle valve downstream pressure as pressure of air within a throttle valve downstream section, which is a portion of the intake passage between the throttle valve and the intake valve, the estimations being performed by use of a throttle valve upstream section model, which is a physical model constructed on the basis of conservation laws for air within the throttle valve upstream section, and a throttle valve downstream section model, which is a physical model constructed on the basis of conservation laws for air within the throttle valve downstream section; second pressure estimation means for estimating, as the throttle valve upstream pressure and the throttle valve downstream pressure, combined section pressure as pressure of air within a combined section, which is a portion of the intake passage between the supercharger and the intake valve, the estimation being performed by use of a combined section model, which is a physical model constructed on the basis of conservation laws for air within the combined section; selection condition determination means for determining whether selection conditions are satisfied, including a throttle valve opening condition that opening of the throttle valve is greater than a predetermined threshold throttle valve opening; and cylinder air quantity estimation means for estimating the cylinder air quantity on the basis of the throttle valve downstream pressure estimated by means of the first pressure estimation means when the selection conditions are not satisfied, and estimating the cylinder air quantity on the basis of the throttle valve downstream pressure estimated by means of the second pressure estimation means when the selection conditions are satisfied. first pressure estimation means for estimating throttle valve upstream pressure as pressure of air within a throttle valve upstream section, which is a portion of the intake passage between the supercharger and the throttle valve, and estimating throttle valve downstream pressure as pressure of air within a throttle valve downstream section, which is a portion of the intake passage between the throttle valve and the intake valve, the estimations being performed by use of a throttle valve upstream section model, which is a physical model constructed on the basis of conservation laws for air within the throttle valve upstream section, and a throttle valve downstream section model, which is a physical model constructed on the basis of conservation laws for air within the throttle valve downstream section; second pressure estimation means for estimating, as the throttle valve upstream pressure and the throttle valve downstream pressure, combined section pressure as pressure of air within a combined section, which is a portion of the intake passage between the supercharger and the intake valve, the estimation being performed by use of a combined section model, which is a physical model constructed on the basis of conservation laws for air within the combined section; selection condition determination means for determining whether selection conditions are satisfied, including a throttle valve opening condition that opening of the throttle valve is greater than a predetermined threshold throttle valve opening; and cylinder air quantity estimation means for estimating the cylinder air quantity on the basis of the throttle valve downstream pressure estimated by means of the first pressure estimation means when the selection conditions are not satisfied, and estimating the cylinder air quantity on the basis of the throttle valve downstream pressure estimated by means of the second pressure estimation means when the selection conditions are satisfied.