3D asymmetric magnetic reconnection is an important investigation of the Space Plasma Environment Research Facility, which is being built as a user facility at the Harbin Institute of Technology in China. Four magnetosheath coils, which consist of Poloidal Field (labeled PF) coils and Toroidal Field (labeled TF) coils, are used to generate the magnetic field and plasma environment for the reconnecting experiment. A capacitor-based pulsed power supply (PPS) system with a modular design is developed to excite the magnetosheath coils to generate the required amplitude and duration of the magnetic field. The PPS system includes the PF PPS and TF PPS, which include four sets of PPSs, respectively. Each set of PF PPS and TF PPS consists of nine modules and four modules, respectively, and each module consists of a charge and discharge unit. The PF PPS can provide a pulsed current of no less than 360 kA for the corresponding PF coil at 0.11ms when the charging voltage is 20 kV, and the duration of the pulsed current from the peak to 10% of the peak is no more than 0.6ms. The TF PPS can provide a pulsed current of no less than 200 kA for the corresponding TF coil at 0.08ms when the charging voltage is 20 kV, and the duration of the pulsed current from the peak to 10% of the peak is no more than 1.6ms. The detailed design of the PPS has been discussed in this paper, and the detailed design of the main components in the discharge unit of the PPS is also given in this paper. Finally, the discharge tests of all the PPSs are carried out to verify the design of the PPSs, and the results of the PPSs in discharge tests indicate that all the PPSs meet the design requirements.