High voltage fracturing technology was widely used in the field of reservoir reconstruction due to its advantages of being clean, pollution-free, and high-efficiency. However, high-frequency circuit oscillation occurs during the underwater high voltage pulse discharge process, which brings security risks to the stability of the pulse fracturing system. In order to solve this problem, an underwater pulse power discharge system was established, the circuit oscillation generation conditions were analyzed and the circuit oscillation suppression method was proposed. Firstly, the system structure was introduced and the charging model of the energy storage capacitor was established by the state space average method. Next, the electrode high-voltage breakdown model was established through COMSOL software, the electrode breakdown process was analyzed according to the electron density distribution image, and the plasma channel impedance was estimated based on the conductivity simulation results. Then the underwater pulse power discharge process and the circuit oscillation generation condition were analyzed, and the circuit oscillation suppression strategy of using the thyristor to replace the gas spark switch was proposed. Finally, laboratory experiments were carried out to verify the precision of the theoretical model and the suppression effect of circuit oscillation. The experimental results show that the voltage variation of the energy storage capacitor, the impedance change of the pulse power discharge process, and the equivalent circuit in each discharge stage were consistent with the theoretical model. The proposed oscillation suppression strategy can not only prevent the damage caused by circuit oscillation but also reduce the damping oscillation time by 77.1%, which can greatly improve the stability of the system. This research has potential application value in the field of underwater pulse power discharge for reservoir reconstruction.