A cylinder intake air amount calculating apparatus for an internal combustion engine that calculates a cylinder intake air amount, which is an amount of fresh air sucked in a cylinder of the engine using an intake air pipe model equation which is obtained by modeling an intake pipe of the engine, is provided. An intake air flow rate is obtained. The cylinder intake air amount is calculated by applying the intake air flow rate and a preceding value of the cylinder intake air amount to the intake pipe model equation. A predicted intake air flow rate which is a predicted value of the intake air flow rate is calculated. A predicted cylinder intake air amount which is a predicted value of the cylinder intake air amount is calculated by applying the predicted intake air flow rate and the cylinder intake air amount to the intake pipe model equation.