Permanent magnet spherical actuator (PMSA) is a multi-variable featured and inter-axis coupled nonlinear system, which unavoidably compromises its motion control implementation. Uncertainties such as external load and friction torque of ball bearing and manufacturing errors also influence motion performance significantly. Therefore, the objective of this paper is to propose a controller based on a single neural adaptive (SNA) algorithm and a neural network (NN) identifier optimized with a particle swarm optimization (PSO) algorithm to improve the motion stability of PMSA with three-dimensional magnet arrays. The dynamic model and computed torque model are formulated for the spherical actuator, and a dynamic decoupling control algorithm is developed. By utilizing the global-optimization property of the PSO algorithm, the NN identifier is trained to avoid locally optimal solution and achieve high-precision compensations to uncertainties. The employment of the SNA controller helps to reduce the effect of compensation errors and convert the system to a stable one, even if there is difference between the compensations and uncertainties due to external disturbances. A simulation model is established, and experiments are conducted on the research prototype to validate the proposed control algorithm. The amplitude of the parameter perturbation is set to 5%, 10%, and 15%, respectively. The strong robustness of the proposed hybrid algorithm is validated by the abundant simulation data. It shows that the proposed algorithm can effectively compensate the influence of uncertainties and eliminate the effect of inter-axis couplings of the spherical actuator.