To meet the demand of irreversible electroporation for nanosecond pulse power supply, this paper proposes a sub-microsecond high voltage pulse power supply with high repetition frequency, which is based on positive Marx circuit and has ns rising time. The pulse power supply uses optical fiber to transmit signals. After the driver chip amplifies the signal, the magnetic core transformer is used to transmit the drive signal to the MOSFET. The magnetic core transformer provides magnetic isolation to the circuit, so that the drive circuit will not be affected by the high voltage output and the withstand voltage level of the circuit is improved. The design of drive circuit is simple, and it requires fewer components. It provides negative bias voltage so that the switch can be reliably turned off and can effectively improve the electromagnetic compatibility. A 16-stage prototype has been built. The experiment showed that 10 kV square pulses were obtained over 10 kΩ resistive load when the input voltage was 630 V. Its minimum pulse width is 300 ns, and the frequency is adjustable from 1 Hz to 10 kHz. The pulse power supply is compact, and can flexibly adjust the voltage amplitude, pulse width and frequency. The influence of the magnetic material and number of turns of the windings of the magnetic core are also studied. The increase of turns ratio will affect the signal pulse width. Under certain conditions, the difference of single turn inductance and magnetic core material have little effect on signal pulse width.