This paper firstly gives a brief description about the principle of resistance-butt welding of nuclear fuel rod, and it points out that the power supply is a key technology for welding process. According to the welding process and the welded material properties, capacitor discharge power supply is devised as welding power supply. The design of charging circuit of single-phase bridge rectifier with SCR and control circuit is finished. The process of power discharge is simulated and the parameters (capacitance C, charging voltage uc) are optimized with Matlab. By the welding experiments, it shows that the output current curve is suitable for resistance-butt welding of nuclear fuel rods, and the test results of welding samples entirely consistent with process requirements.