An air quantity estimation apparatus for an internal combustion engine having an intake passage for introducing air taken from outside of the engine into a cylinder; a throttle valve which is disposed in said intake passage and whose opening is adjustable for changing quantity of air passing through the intake passage; a supercharger including a compressor disposed in said intake passage at a position upstream of said throttle valve for compressing the air in said intake passage; and an intercooler disposed in said intake passage between said throttle valve and said supercharger for cooling air in said intake passage, characterized in that the air quantity estimation apparatus comprises: intercooler-internal air condition estimation means for estimating pressure and temperature of the air in the intercooler as pressure and temperature of throttle valve upstream air which is air at a position upstream of said throttle valve in said intake passage, respectively, by use of a physical model configured on the basis of a mass conservation law and an energy conservation law with respect to the air in the intercooler, the physical model being designed in consideration of a first energy imparted by said supercharger to air supplied into said intercooler, and a second energy exchanged between a wall of the intercooler and the air in the intercooler; cylinder intake-air quantity estimation means for estimating, on the basis of the estimated pressure of the throttle valve upstream air and the estimated temperature of the throttle valve upstream air, cylinder intake-air quantity which is quantity of air introduced into said cylinder, wherein said intercooler-internal air condition estimation means is configured so as to estimate said first energy on the basis of a rotational speed of the compressor of said supercharger, and a pressure (Pa) and temperature (Ta) of air in the intake passage at a position upstream of the compressor, the air quantity estimation apparatus further comprising compressor rotational speed-detection means for detecting said rotational speed of the compressor of the supercharger; said intercooler-internal air condition estimation means is configured so as to estimate said first energy at a future point in time later than a present point in time on the basis of said detected rotational speed of the compressor, and to estimate, by adopting the estimated first energy at the future point in time as said first energy which is used in said physical model, the pressure and the temperature of the air in the intercooler at the future point in time as the pressure and the temperature of the throttle valve upstream air at the future point in time, respectively; and said cylinder intake-air quantity estimation means is configured so as to estimate the cylinder intake-air quantity at the future point in time on the basis of the estimated pressure and the estimated temperature of the throttle valve upstream air at the future point in time. intercooler-internal air condition estimation means for estimating pressure and temperature of the air in the intercooler as pressure and temperature of throttle valve upstream air which is air at a position upstream of said throttle valve in said intake passage, respectively, by use of a physical model configured on the basis of a mass conservation law and an energy conservation law with respect to the air in the intercooler, the physical model being designed in consideration of a first energy imparted by said supercharger to air supplied into said intercooler, and a second energy exchanged between a wall of the intercooler and the air in the intercooler; cylinder intake-air quantity estimation means for estimating, on the basis of the estimated pressure of the throttle valve upstream air and the estimated temperature of the throttle valve upstream air, cylinder intake-air quantity which is quantity of air introduced into said cylinder, wherein said intercooler-internal air condition estimation means is configured so as to estimate said first energy on the basis of a rotational speed of the compressor of said supercharger, and a pressure (Pa) and temperature (Ta) of air in the intake passage at a position upstream of the compressor, the air quantity estimation apparatus further comprising compressor rotational speed-detection means for detecting said rotational speed of the compressor of the supercharger; said intercooler-internal air condition estimation means is configured so as to estimate said first energy at a future point in time later than a present point in time on the basis of said detected rotational speed of the compressor, and to estimate, by adopting the estimated first energy at the future point in time as said first energy which is used in said physical model, the pressure and the temperature of the air in the intercooler at the future point in time as the pressure and the temperature of the throttle valve upstream air at the future point in time, respectively; and said cylinder intake-air quantity estimation means is configured so as to estimate the cylinder intake-air quantity at the future point in time on the basis of the estimated pressure and the estimated temperature of the throttle valve upstream air at the future point in time.