A drive system for a construction machine capable of appropriately controlling a distribution flow rate to each hydraulic actuator and improving operability by an operator is provided. A flow rate distribution section that computes a distribution flow rate of a hydraulic fluid supplied to each of a plurality of hydraulic actuators on the basis of a demanded flow rate, sets, within a distributable region set for computing a range of a distributable flow rate that is a flow rate of the hydraulic fluid suppliable to each of at least two hydraulic actuators driven by a combined operation among the plurality of hydraulic actuators from a plurality of hydraulic pump devices for the at least two hydraulic actuators, a distribution region for computing a range of the distribution flow rate of the hydraulic fluid actually supplied to each of the at least two hydraulic actuators, and computes the distribution flow rate in such a manner that the distribution flow rate falls within the distribution region and a ratio among the distribution flow rates of the plurality of hydraulic actuators is equal to a ratio among the demanded flow rates of the plurality of hydraulic actuators.