Pump control systems are widely used, because of their energy saving properties and their high efficiency. Nevertheless, pump control systems generally have a low accuracy, because of the nonlinear pump flow and other nonlinearities of hydraulic systems. Furthermore, due to the underlaying high order dynamics, pump control systems have low response times, which is one of the main drawbacks. Servo motor-pump direct driven systems are commonly used in today’s industry. The application of servo motor pumps allow a reliable performance with quick response times. For low speeds, however, servo motor pumps do not achieve a high accuracy due to the pump flow deviation. The goal of this paper is to present a controller for a servo motor-pump direct driven system, which improves the accuracy especially at low pump speeds. For that purpose, the controller uses a nonlinear flow mapping, which maps the desired pump flow and pump pressure to the voltage input for the motor-pump. Additionally, the controller uses a backstepping method, which tracks the position as a first step and regulates the pressure as a second step. Comparison experiments to a controller without nonlinear flow mapping show that the controller designed in this paper has improved performances and tracking accuracy.