Shanghai high repetition rate X-ray free electron laser and extreme light (SHINE) project is a superconducting linear electron accelerator-based facility under construction at the Shanghai Advance Research Institute, Chinese Academy of Sciences. It provides electron beam bunches with an energy of 8 GeV and requires a beam distribution system to switch at a repetition rate of 1 MHz between three undulator lines and a dump. This article presents the unique challenges of designing a pulsed power supply for the kicker magnet in the SHINE facility at a high repetition of 1 MHz. A fast pulse forming topology on the basis of inductor, resistor, and capacitor second-order circuit aiming for a kicker magnet was proposed. The mathematical models of the peak current of the kicker magnet, time transient at the peak current were derivated, and subsequently applied to determine the key parameters in the circuit design. Experimental results demonstrate a pulse-to-pulse amplitude stability of 108 ppm, a pulse width less than 1 μs and a peak current of ∼44.1 A at a repetition rate of 1 MHz. These findings are in corresponding to the design parameters proposed for the project.