1. An air amount inside cylinder detection apparatus for an internal combustion engine, comprising: an intake air flow amount detection means for detecting a flow amount of intake air flowing through an intake air passageway; a response delay compensation means for compensating a response delay of said intake air flow amount detection means; and a calculation means for calculating an air amount inside cylinder, wherein said calculation means uses an intake air system model modeling a behavior of the intake air passing through a throttle valve and flowing into cylinders, said intake air system model receives an output of said response delay compensation means so as to calculate an output of said intake air system model as the air amount inside cylinder.