Fuel pressure control apparatus of internal combustion engine

A fuel pressure control apparatus and method controls a pressure of fuel that is delivered from a fuel pump (47) to a fuel pipe (53) in an internal combustion engine (11) of a vehicle. A controller (92) of the fuel pressure control apparatus calculates a controlled variable based on at least an integral term that is updated in accordance with a difference between an actual fuel pressure in the fuel pipe and a target value thereof, and controls an amount of the fuel delivered from the fuel pump in a feedback manner, using the controlled variable, so that the actual fuel pressure approaches the target value. During the control of the fuel pressure, the controller inhibits updating of the integral term to a value that results in an increase in the amount of the fuel delivered from the fuel pump, when the amount of the fuel delivered is approximate to or equal to a maximum value thereof.