The inductive energy storage for pulsed power supplies is considered to have a greater potential for high energy density than that of capacitive one. Therefore, it has practical applications in the industrial and military fields. Associating with the superconducting technology, this paper proposes an inductive pulsed power supply based on the head-to-tail series model of high-temperature superconducting air-core pulsed transformer. First, designed structure and working processes are analyzed in detail. Then, the simulated circuit model is built to illustrate the principles and characteristics using the software SIMPLORER. For verifying the feasibility of this pulsed power supply and gaining some experience in practical operation, a small-scale experiment is carried out with different delay times between two controlled switches. The experimental results show that large pulsed current with high energy transfer efficiency can be achieved by this model, which provides some guidance for future work.