Provided is a work machine driving device which can reduce unnecessary switching control of switching valves. The present invention is configured so that at least two closed-circuit hydraulic pumps 2a to 2f can be connected in a closed loop to any one of hydraulic actuators 7a to 7c, 10c through electromagnetic switching valves 12, in which a controller 16 includes a priority order calculating circuit 31 which calculates the allocation of the closed-circuit hydraulic pumps 2a to 2f to the hydraulic actuators 7a to 7c, 10c according to operation of operation levers 17a, 17b and a priority order map 32 determining priority connection relationships between the closed-circuit hydraulic pumps 2a to 2f and the hydraulic actuators 7a to 7c, 10c, and the priority order calculating circuit 31 selects and allocates an unallocated closed-circuit hydraulic pump 2a to 2f when the number of closed-circuit hydraulic pumps 2a to 2f to be allocated increases.