An electrically driven hydraulic work machine comprising: an electric motor, a hydraulic pump driven by the electric motor, and a controller that controls a revolution speed of the electric motor on a basis of a target revolution speed of the electric motor, and drives the hydraulic pump to carry out work, wherein the electrically driven hydraulic work machine comprises: a maximum allowable power setting device that sets maximum allowable power (Pwmax) allowed to be consumed by the electric motor, a pressure sensor that senses a delivery pressure of the hydraulic pump, and a target revolution speed instruction device that makes an instruction of the target revolution speed (Nac) of the electric motor, and the controller is configured to calculate target power (Pwac) to be consumed by the hydraulic pump on a basis of capacity (q) of the hydraulic pump, the delivery pressure of the hydraulic pump sensed by the pressure sensor, and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, calculate a first target revolution speed (Nreg) of the electric motor on a basis of lower one of the target power (Pwac) and the maximum allowable power (Pwmax) set by the maximum allowable power setting device, select, as a second target revolution speed (Nd), a lower one of the first target revolution speed (Nreg) and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, and control the revolution speed of the electric motor on a basis of the second target revolution speed (Nd) in such a manner that the target power (Pwac) falls within a range of the maximum allowable power (Pwmax). an electric motor, a hydraulic pump driven by the electric motor, and a controller that controls a revolution speed of the electric motor on a basis of a target revolution speed of the electric motor, and drives the hydraulic pump to carry out work, wherein the electrically driven hydraulic work machine comprises: a maximum allowable power setting device that sets maximum allowable power (Pwmax) allowed to be consumed by the electric motor, a pressure sensor that senses a delivery pressure of the hydraulic pump, and a target revolution speed instruction device that makes an instruction of the target revolution speed (Nac) of the electric motor, and the controller is configured to calculate target power (Pwac) to be consumed by the hydraulic pump on a basis of capacity (q) of the hydraulic pump, the delivery pressure of the hydraulic pump sensed by the pressure sensor, and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, calculate a first target revolution speed (Nreg) of the electric motor on a basis of lower one of the target power (Pwac) and the maximum allowable power (Pwmax) set by the maximum allowable power setting device, select, as a second target revolution speed (Nd), a lower one of the first target revolution speed (Nreg) and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, and control the revolution speed of the electric motor on a basis of the second target revolution speed (Nd) in such a manner that the target power (Pwac) falls within a range of the maximum allowable power (Pwmax). a maximum allowable power setting device that sets maximum allowable power (Pwmax) allowed to be consumed by the electric motor, a pressure sensor that senses a delivery pressure of the hydraulic pump, and a target revolution speed instruction device that makes an instruction of the target revolution speed (Nac) of the electric motor, and the controller is configured to calculate target power (Pwac) to be consumed by the hydraulic pump on a basis of capacity (q) of the hydraulic pump, the delivery pressure of the hydraulic pump sensed by the pressure sensor, and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, calculate a first target revolution speed (Nreg) of the electric motor on a basis of lower one of the target power (Pwac) and the maximum allowable power (Pwmax) set by the maximum allowable power setting device, select, as a second target revolution speed (Nd), a lower one of the first target revolution speed (Nreg) and the target revolution speed (Nac) of the electric motor instructed by the target revolution speed instruction device, and control the revolution speed of the electric motor on a basis of the second target revolution speed (Nd) in such a manner that the target power (Pwac) falls within a range of the maximum allowable power (Pwmax).