The single-switch resonant circuit can generate high-voltage pulses using only one switch, however, when the switch is turned off at a positive resonant current, a turn-off overvoltage is generated, which damages the switch. To solve this problem, the RCD (Resistance-Capacitance-Diode) snubber circuit is paralleled with the switch or the R-D (Resistance-Diode) freewheeling branch is paralleled with the primary side of the transformer. However, under high-voltage pulse conditions, the loading characteristics and effects of the two overvoltage suppression circuits under different loads are still unclear. This study compares and analyzes the overvoltage suppression mechanism, parameter selection basis, overvoltage suppression effect and the components power loss of the two circuits. The results show that the overvoltage of the power supply switch with R-D branch is proportional to the leakage inductance current and the resistance R of the branch. If R is larger, its overvoltage coefficient is larger than that of the power supply with RCD absorption circuit. And if R is smaller, the components power loss is large. In a high-voltage pulse power supply, the capacitance of the RCD snubber circuit does not need to discharge the power. Due to the limitation of leakage inductance, when the resonant pulse circuit is short-circuited, the current is not too large to burn the switch. When driving the capacitive dielectric barrier discharge, the current can be reversed automatically to achieve zero current shutdown.