A hydraulic drive system of a work machine comprising: - an engine; - first and second hydraulic pumps (P1, P2) driven by the engine; - first and second pump hydraulic lines (L1, L2) to which a delivered hydraulic fluid from the respective first and second hydraulic pumps (P1, P2) is supplied; - at least one first actuator driven by the hydraulic fluid supplied from the first pump hydraulic line; - a plurality of second actuators (8, 10) including a specific actuator driven by the hydraulic fluid supplied from the second pump hydraulic line; - a first directional control valve provided in the first pump hydraulic line and controlling a flow rate of the hydraulic fluid supplied to the first actuator; - a plurality of second directional control valves (V1, V3) provided in the second pump hydraulic line and each controlling the flow rate of the hydraulic fluid supplied to the plurality of second actuators (8, 10) including the specific actuator; - a plurality of operation devices (19, 20, 21) operating the first actuator and the plurality of second actuators (8, 10) including the specific actuator by respectively switch-operating the first directional control valve and the plurality of second directional control valves (V1, V3); - an electric motor; - a third hydraulic pump driven by the electric motor; - a third pump hydraulic line to which a delivered hydraulic fluid from the third hydraulic pump is supplied; - a plurality of operation amount devices detecting operation amounts of the plurality of operation devices (19, 20, 21); - a control device drive-controlling the electric motor in accordance with an operation of the plurality of second actuators (8, 10); and characterized by further comprising: - a third directional control valve provided in the third pump hydraulic line, switch-operated by a specific operation device of the plurality of operation devices (19, 20, 21) that operates the specific actuator of the plurality of second actuators (8, 10), and controlling the flow rate of the hydraulic fluid supplied to the specific actuator from the third hydraulic pump; and the control device drives the third hydraulic pump by the electric motor when a combined operation of two or more second actuators (8, 10) including the specific actuator of the plurality of second actuators (8, 10) is detected by the plurality of operation amount detection devices. - an engine; - first and second hydraulic pumps (P1, P2) driven by the engine; - first and second pump hydraulic lines (L1, L2) to which a delivered hydraulic fluid from the respective first and second hydraulic pumps (P1, P2) is supplied; - at least one first actuator driven by the hydraulic fluid supplied from the first pump hydraulic line; - a plurality of second actuators (8, 10) including a specific actuator driven by the hydraulic fluid supplied from the second pump hydraulic line; - a first directional control valve provided in the first pump hydraulic line and controlling a flow rate of the hydraulic fluid supplied to the first actuator; - a plurality of second directional control valves (V1, V3) provided in the second pump hydraulic line and each controlling the flow rate of the hydraulic fluid supplied to the plurality of second actuators (8, 10) including the specific actuator; - a plurality of operation devices (19, 20, 21) operating the first actuator and the plurality of second actuators (8, 10) including the specific actuator by respectively switch-operating the first directional control valve and the plurality of second directional control valves (V1, V3); - an electric motor; - a third hydraulic pump driven by the electric motor; - a third pump hydraulic line to which a delivered hydraulic fluid from the third hydraulic pump is supplied; - a plurality of operation amount devices detecting operation amounts of the plurality of operation devices (19, 20, 21); - a control device drive-controlling the electric motor in accordance with an operation of the plurality of second actuators (8, 10); and characterized by further comprising: - a third directional control valve provided in the third pump hydraulic line, switch-operated by a specific operation device of the plurality of operation devices (19, 20, 21) that operates the specific actuator of the plurality of second actuators (8, 10), and controlling the flow rate of the hydraulic fluid supplied to the specific actuator from the third hydraulic pump; and the control device drives the third hydraulic pump by the electric motor when a combined operation of two or more second actuators (8, 10) including the specific actuator of the plurality of second actuators (8, 10) is detected by the plurality of operation amount detection devices. - a third directional control valve provided in the third pump hydraulic line, switch-operated by a specific operation device of the plurality of operation devices (19, 20, 21) that operates the specific actuator of the plurality of second actuators (8, 10), and controlling the flow rate of the hydraulic fluid supplied to the specific actuator from the third hydraulic pump; and