A work machine pump control system equipped with at least one actuator (9, 109, 87, 88, 89, 92, 93) driving a driven member (84, 85, 86, 91, 94), a hydraulic pump that is a variable displacement type and of a bent axis type and that delivers a hydraulic fluid for driving the actuators (9, 109, 87, 88, 89, 92, 93), at least one control valve controlling the hydraulic fluid to be supplied to a corresponding actuator (9, 109, 87, 88, 89, 92, 93) from the hydraulic pump, at least one pilot operation type operation device generating an operation pressure (px) in accordance with an operation and outputting the operation pressure (px) thus generated to a corresponding control valve, a pilot pump generating an initial pressure of the operation pressure (px), at least one operation pressure sensor (7; 107) detecting an operation pressure (px) of a corresponding operation device, and at least one load pressure sensor (6; 106) detecting the pressure of a line connecting the hydraulic pump and the actuators (9, 109, 87, 88, 89, 92, 93) as a load pressure (py), characterized in that the work machine pump control system comprises: a pump horsepower control valve that causes a first urging force determining a limited horsepower of the hydraulic pump and a second urging force due to a delivery pressure of the hydraulic pump to act on a spool in opposition to each other and that controls capacity of the hydraulic pump such that a pump absorption horsepower does not exceed the limited horsepower; a target pump flow rate computation section (42; 142) computing a target pump flow rate (Qtar) of the hydraulic pump on the basis of an operation pressure (px) detected by the at least one operation pressure sensor (7; 107) and a load pressure (dy) detected by the load pressure sensor (6; 106); a target horsepower computation section (41; 141) that computes a required horsepower (Freq) corresponding to the detected operation pressure (px) from a relationship related to the operation pressure (px) of a corresponding operation device and that computes a target horsepower (Ftar) based on the required horsepower (Freq); and a pump horsepower control section that controls the pump horsepower control valve, based on a target pump flow rate (Qtar) computed by the target pump flow rate computation section (42; 142) and on a target horsepower (Ftar) computed by the target horsepower computation section (41; 141), such that the target pump flow rate (Qtar) is delivered with the limited horsepower determined by the pump horsepower control valve. a pump horsepower control valve that causes a first urging force determining a limited horsepower of the hydraulic pump and a second urging force due to a delivery pressure of the hydraulic pump to act on a spool in opposition to each other and that controls capacity of the hydraulic pump such that a pump absorption horsepower does not exceed the limited horsepower; a target pump flow rate computation section (42; 142) computing a target pump flow rate (Qtar) of the hydraulic pump on the basis of an operation pressure (px) detected by the at least one operation pressure sensor (7; 107) and a load pressure (dy) detected by the load pressure sensor (6; 106); a target horsepower computation section (41; 141) that computes a required horsepower (Freq) corresponding to the detected operation pressure (px) from a relationship related to the operation pressure (px) of a corresponding operation device and that computes a target horsepower (Ftar) based on the required horsepower (Freq); and a pump horsepower control section that controls the pump horsepower control valve, based on a target pump flow rate (Qtar) computed by the target pump flow rate computation section (42; 142) and on a target horsepower (Ftar) computed by the target horsepower computation section (41; 141), such that the target pump flow rate (Qtar) is delivered with the limited horsepower determined by the pump horsepower control valve.