A high-pressure fuel supply system and method are used with an internal combustion engine that includes a pressure raising mechanism (10, 20) operable to raise a pressure in a high-pressure portion of the fuel supply system to a level suitable for starting the engine, and a high-pressure pump (7) operable to raise the pressure in the high-pressure portion to a target level that is higher than the above level after the engine is started. When the pressure in the high-pressure portion reaches the level suitable for starting the engine, a pressure wall of the pressure raising mechanism displaces over only a part of its displacement range that ranges from an original position to a maximum displacement position, so that the pressure wall will be able to further displace toward the maximum displacement position so as to raise the pressure in the high-pressure portion when the engine is re-started after the engine is stopped before the pressure wall is returned to the original position.