An engine control apparatus and an engine control method for a vehicle are disclosed. The engine control apparatus includes: an integrated thermal management valve in which an opening degree of a plurality of valves is adjusted by rotation of a cam; a storage to store an opening degree of the integrated thermal management valve based on a road slope and a transmission gear value; and a controller that controls the opening degree of the integrated thermal management valve by using an engine revolutions per minute (RPM) and an accelerator pedal value. In particular, when the accelerator pedal value is smaller than a predetermined threshold, the controller controls the opening degree of the integrated thermal management valve based on the road slope and the transmission gear value.