Taking into comprehensive consideration the tracking performance, energy consumption, and stability requirements of underwater unmanned vehicles (UUVs), this paper investigates a novel stability-constrained-based multi-objective particle swarm optimization (SC-based MOPSO) algorithm. Firstly, a disturbance observer is designed to estimate system disturbances. To tackle the state constraint problem, by leveraging barrier Lyapunov functions and the backstepping method, the controller design problem, which aims to guarantee both system constraints and stability, is reformulated as a controller gain constraint problem. Secondly, by taking system tracking error, energy consumption, disturbance observer estimation error, and gain magnitude as performance indicators, a multi-objective optimization model for the UUV anti-disturbance control problem is established. Subsequently, the constrained problem is incorporated into the performance index calculation in the form of a penalty term during the optimization process. This algorithm is employed to optimize the control and disturbance observer gains. Finally, through comparisons with other multi-objective optimization algorithms and gains obtained via the traditional linear matrix inequality method, the proposed SC-based MOPSO algorithm is shown to achieve better control performance while ensuring state constraints.