Aiming at the problem of unstable output power of wireless charging systems for autonomous underwater vehicles (AUVs), a magnetic coupler (MC) with an arc-shaped core structure is introduced and an output power stabilization control strategy based on mutual inductance identification algorithm is proposed. Firstly, an arc-shaped MC with high tolerances, excellent magnetic coupling and weak electromagnetic interference (EMI) is designed for the cylinder-shaped AUV. Based on ANSYS Maxwell simulation, an analysis of the magnetic field and comparative misalignment tests are carried out for the arc-shaped and the double dipole core structures. Secondly, a mathematical model of the LCC-S type magnetically coupled resonant wireless power transfer (MCR-WPT) system is developed, and a particle swarm parameter identification algorithm with adaptive inertia weights is proposed. Finally, the output power is steadily controlled by real-time adaptation of the duty cycle for the Buck-Boost circuit. The results show there is a maximum error within 2.5% in mutual inductance identification when the load is changed from 0 Ω to 12 Ω and the mutual inductance is changed from 25 μH to 50 μH. The system output power is steady at around 680 W with a maximum fluctuation rate of 4.90%, which verifies the efficiency of the power stabilization control strategy.