The purpose of this paper is to develop a new control method for a hydraulic elevator equipped with a variable-speed bidirectional fixed-displacement pump and a converter-fed electric machine operating in torque regulation mode. Conventional hydraulic elevators use a bypass throttle valve to divert excess flow during upwards motion and restrict flow during downwards motion, resulting in wasted energy and fluid heating, whereas the proposed approach manipulates flow by varying the speed of the pump, thereby influencing motion in an energy efficient manner. A primary focus of this investigation has been to keep both the physical system and its controller as simple as possible, while meeting performance and robustness goals. All essential modeling and control details are provided, as well as a summary of extensive simulation results demonstrating the effectiveness of the proposed control method.