Abstract In this study, a method of combining Flowmaster and ANSYS CFX software was adopted. Based on the consistency between the numerical calculation results of the hydraulic performance of a centrifugal pump and the test results, an operating model of a centrifugal pump system is established, variation law of the external characteristic parameters in the transient process is obtained, and different acceleration times and modes are set. The change law of the transient external characteristics and the evolution mechanism of the internal flow field during the variable speed regulation and acceleration of the centrifugal pump are disclosed. By introducing a control system evaluation index, the effects of acceleration time and mode on performance and internal flow field of variable speed control process of the centrifugal pump are analysed in detail. The results show that the turbulent kinetic energy in the pump changes violently, and the high turbulent kinetic energy and high vorticity are widely distributed, which has an obvious transient effect. An exponential acceleration method can effectively reduce the peak value and overshoot of external characteristic parameters while reducing the speed regulation time.