A hydraulic drive system comprises a controller (12) and several condition sensors. A boom-up target flow rate setting section determines a boom-up target flow rate based on signals from a pressure sensor (11) and a rotational speed meter (16), a pump delivery rate detecting section determines a pump delivery rate based on signals from a tilt angle sensor (15) and the rotational speed meter (16), a differential pressure detecting section and a center bypass flow rate calculating section determine a center bypass flow rate based on signals from pressure sensors (9, 10), a boom cylinder calculating section determines a boom cylinder flow rate from the pump delivery rate and the center bypass flow rate, and a first pump target displacement volume calculating section calculates a first pump target tilt angle .theta..sub.1 in accordance with the difference between the boom-up target flow rate and the boom cylinder flow rate. In this case, .theta..sub.1 is larger than a second pump target tilt angle .theta..sub.2 for negative control and is selected by a maximum value selecting section. Then, a minimum value selecting section selects the smaller one of .theta..sub.1 and a maximum tilt angle .theta..sub.max determined with horsepower control, and drive signal generating section outputs a corresponding target current to a solenoid proportional valve (13) for driving a piston (6a) of a regulator (6) to the right in FIG. 4.