With the continuous improvement of high power density, fast charging rate, and miniaturization requirements of pulse power supplies, a high-voltage constant current (HCC) charging power supply suitable for fast charging of pulse capacitors is developed. The low-voltage cascade topology structure is employed, which achieves high-voltage output. To achieve constant current control, a combined modulation strategy based on PWM carrier phase shifting and carrier stacking is utilized. This modulation method can reduce output current ripple, switch losses, and inductance, which are all factors improving the power density of HCC charging power supply. Firstly, the working principle of the power system is analyzed. Secondly, the simulation models are set up in MATLAB, and the simulation results verified the feasibility of the control strategy. Finally, the developed power supply was subjected to high-voltage experiments under 0.3F capacitor load, and the experimental results showed that the constant current output effect of the power supply was good and the operation was reliable.