The instantaneous high-voltage characteristic of the pulsed power supply can effectively generate high-density plasma, increase the rate of plasma chemical reaction, and reduce the energy loss. For the application requirements of high-voltage pulsed discharge and low-temperature plasma, this paper designs a high-voltage pulsed power supply based on an inductance-isolated Marx circuit. The main circuit of this power supply adopts the classical Marx principle of capacitor charging in parallel and discharging in series, uses diodes instead of isolation resistors, and adds a boost current-limiting inductor in front of the first-stage Marx circuit, and uses insulated gate bipolar transistors (IGBTs) as the switching device, with each stage consisting of IGBTs, high-voltage diodes, and inductorless capacitors. The feasibility of the two driving schemes of optocoupler floating drive and transformer drive are designed and verified respectively, and the experiments show that the transformer drive scheme is more feasible. Accordingly, a 20-stage Marx high-voltage pulse power supply was constructed, which can realize 12 kV pulse output, pulse width of 4–12 us, pulse frequency of 1–5 kHz, and is successfully applied to argon medium blocking jet discharge.