Unmanned Aerial Vehicle (UAV) are increasingly utilized in power line inspection work, the 3D path planning for UAV urgently needs to be addressed. Artificial Fish Swarm Algorithm (AFSA) is one of the most common used methods for the 3D path planning of UAVs, but the problems of rapid convergence and susceptibility to less optimal solutions for AFSA needs to be solved. For this reason, a 3D path planning method for power inspection UAVs based on an Improved Artificial Fish Swarm Algorithm (IAFSA) is proposed in this paper. This algorithm references the metropolis criterion of the Simulated Annealing (SA) algorithm and introduces an anti-Metropolis criterion to escape from less optimal solutions. Firstly, a 3D mountainous terrain model is constructed based on the environment where power inspection UAV perform inspection tasks in mountainous areas. Then, the anti-Metropolis criterion is introduced into AFSA to escape from less optimal solutions. Finally, to satisfy the performance constraints of the UAV, a cubic spline interpolation function is used to smooth the path. Comparative simulation experiments with Particle Swarm Optimization (PSO), SA, and AFSA are carried out. The result shows that IAFSA proposed in this paper not only exhibits superior optimization performance in different terrain environments, but also maintains the rapid convergence and optimization accuracy of AFSA.