The present invention provides an intake air amount control apparatus for an engine and a control method of an intake air amount of an engine, in which, when the atmospheric pressure exceeds a threshold value, a target lift amount of an intake valve is determined based on a target intake air amount and an electronically controlled throttle is controlled to generate a target boost pressure. On the other hand, when the atmospheric pressure does not exceed the threshold value because of a vehicle traveling at a high altitude, the target lift amount of the intake valve is fixed to a maximum lift amount and the opening angle of the electronically controlled throttle is determined in response to the target intake air amount. Consequently, an actual intake air amount is controlled to be brought to the target intake air amount thereby generating negative pressure necessary for exhaust gas recirculation.