Aimed at the problems of insufficient search range and optimization performance in 3D path planning of unmanned aerial vehicles (UAVs), and the lack of optimization accuracy of the existing slime mould algorithm (SMA), which is easy to fall into local optimization, a 3D path planning method for UAV based on adaptive slime mould algorithm optimization is proposed. First, according to the actual environment that the UAV passes through, the 3D terrain, the threat source and the constraints of the AUV were established. Next, for the problem of insufficient search range, an improved Logistic chaotic map is designed to increase the diversity of the population and expand the search range, which improves the global search ability of SMA. Then, a nonlinear adaptive inertia weight factor is designed to change the linear convergence method into nonlinear convergence, and the weight value is used to update the position of the slime mould, which improves the convergence speed. Finally, in the later stage of the algorithm, the adaptive cauchy mutation is designed, which increases the search space of the slime mould and improves the optimization accuracy. The experimental results show that GSMA has a shorter and smoother path, a faster convergence, a higher optimization accuracy, and a lower energy consumption compared with the gray wolf optimizer (GWO) algorithm, the SMA, and the seagull algorithm (SOA), which further improves the path planning capability of the UAV.