Path planning is crucial for achieving efficient and safe docking of underactuated autonomous underwater vehicles (AUVs). This study proposes a path planning method for underactuated AUV docking based on a novel random partial-particle swarm optimization algorithm (RP-PSO). The method employs a Bézier curve to generate an initial path that satisfies the AUV’s attitude constraints. Then, the generated path is optimized considering path length, curvature, and obstacle avoidance. In the proposed RP-PSO algorithm, a random selection mechanism is introduced to select the partial optimal particle to guide the motion of particles, which enhances the searching ability. Comprehensive simulations are conducted to evaluate the effectiveness of the proposed path planning method by comparing with other three algorithms, and the robustness and stability are validated through Monte-Carlo tests. Simulation results demonstrate the effectiveness of the proposed path-planning method and the RP-PSO algorithm outperforms other compared algorithms in global search capability, stability and convergence speed.