To establish a control method for variable discharge amount high-pressure pump, having good controllability for the pressure in a pressure accumulation chamber and supplying a high-pressure fuel to the pressure accumulation chamber.

A pressure chamber 23a is provided to such in and feed by pressure a low- pressure fuel with expansion and contraction of the capacity, and on the way of a flow passage leading from a low-pressure pump P1 to the pressure chamber 23a, a control valve 6a and check valve 4a are installed in a positional sequence as named from the upstream, and when the capacity of the pressure chamber 23a is enlarged, the fuel is sucked into the pressure chamber 23a in a period starting from closing of the control valve 6a until the opening of the check valve 4a, and with this variable discharge amount high-pressure pump, occurrence of a phenomenon where the air pressure sinks from the feed pressure after closing of the control valve 6a to cause an air expansion is avoided, so that the fuel is extruded to the pressure chamber 23a which is likely to be put in the state with excessive fuel, and to preclude an overpressure feed, opening of the control valve 6a is inhibited, if the pressure in a pressure accumulation chamber is higher than the target by a width above the allowable value, so that the air mixed in the fuel fed from the pump P1 is hindered from entering the upstream of the check valve 4a.