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Higher energy density makes inductive energy storage more promising than capacitive storage for pulsed power supplies in industrial and military fields. To realize high amplitude of pulsed current and relieve stress of opening switch, this paper proposes a novel inductive pulsed power supply consisting of high-temperature superconducting pulse power transformer and ZnO-based nonlinear resistor. First, working processes and laboratory setup are described in detail. Then, simulation using the software SIMPLORER is built to show major pulse characteristics and comparisons of two different nonlinear resistors. For verifying the feasibility of this mode, high-current testing is carried out and the results show that large amplitude of pulsed current 3 kA with energy transfer efficiency 60% is achieved, and the ZnO-based nonlinear resistor can help to limit the voltage of the opening switch to a small constant below its clamping value as current is interrupted.