Inductive energy storage for pulsed power supplies is considered to have great potential because its energy density is 1 order of magnitude higher than that of capacitive one. Associating with the superconducting technology and the STRETCH meat grinder circuit, which proposed by the Institute of Advanced Technology, a superconducting inductive pulsed power supply (SPPS) circuit has been proposed by using an air-core high-temperature superconducting pulsed power transformer (HTSPPT) in our previous study. It can not only recapture the energy in the leakage flux and slow down the current change in inductors by using a capacitor, but also reduce the coil loss and the power requirement of the primary source by using superconducting inductors. However, it can be found that the SPPS may generate a large residual current during the discharging phase, which results in an adverse influence on the working frequency and the energy transfer efficiency of the whole system. This paper proposes a modified circuit based on the bridge current switching circuit and HTSPPT. The main principle of the circuit is that the recaptured energy in the capacitor and the residual energy in the secondary are used to precharge the primary inductor for the next cycle, which shortens the charging time, generates continuous current pulses, and improves the energy transfer efficiency. The procedure of the repetitive SPPS is analyzed in detail, and simulations are carried out to explain how the circuit works clearly.