In an internal combustion engine provided with a high-pressure fuel pump, if the discharging rate of the high-pressure fuel pump is greater than the injection quantity of fuel injected from a injector with the high-pressure fuel pump remaining uncontrollable due to failure or the like, it is probable that the fuel pressure in a common rail unintentionally rises to affect the injector. A high-pressure fuel supply apparatus is provided to solve such a problem. A high-pressure fuel supply apparatus according to the present invention is configured such that if the high-pressure fuel supply apparatus or a control apparatus thereof causes malfunction to increase the pressure in the common rail, the pressure in the common rail does not exceed pressure affecting the flow characteristic and spray characteristic of the injector after recovery from the malfunctioning state.