The start-up process of a high-speed centrifugal pump is typically nonlinear. Traditional proportional-integral-differential (PID) controllers and sliding mode controllers (SMC) suffer from problems such as large speed overshoot, slow approach to sliding mode surfaces, poor stability and system chattering. In order to mitigate these issues and improve the control performance during start-up, a new fuzzy sliding mode controller is proposed in this work. A nonlinear mathematical model of the start-up process of the high-speed centrifugal pump is first established. A new sliding mode reaching law is then designed using a nonlinear power combination function and a hyperbolic tangent function, and the stability of the system is proved. A fuzzy algorithm is then introduced to adjust the coefficient of the reaching law in real time, so that the reaching process is dynamically controlled, and the performance of the controller is further optimized. Finally, a simulation model is built in Simulink for experimental verification. The results show that after incorporating the new fuzzy sliding mode controller, the dynamic response of the centrifugal pump system during start-up is fast, and it quickly converges to a stable state without overshoot. Furthermore, it exhibits good anti-chattering performance and strong robustness to external load disturbances.