The fast cycle full energy storage pulse power supply for the High Intensity heavy ion Accelerator Facility-Booster Ring (HIAF-BRing) needs to maintain extremely high control accuracy in a very wide range of output voltage. For this reason, the power supply adopts the topology of high voltage power units and low voltage power unit in series. The low voltage power unit is used in low voltage stage, after voltage rises, it is switched to high voltage power units, thus high precision output of current at all stages is realized through high voltage and low voltage switching control. However, in the test of prototype, it is found that there is an oscillation problem at switching point, resulting in that the absolute error of output current at switching point cannot meet the requirements. In this paper, a switching point smoothing control algorithm is proposed to smooth switching point duty cycle, and the simulation results are given. The effectiveness of high voltage and low voltage switching control method and its switching point smoothing control algorithm is verified on the HIAF-BRing fast cycle full energy storage pulse power supply prototype. The experimental results show that the absolute error of output current of 100 A injection platform is reduced from ±500 mA to ±50 mA, the absolute error of output current at switching point of 100 A injection platform is reduced from ±1.16 A to ±120 mA, and the problem of low output accuracy of 100 A injection platform is solved.