The path planning algorithm was proposed for multiple unmanned aerial vehicles in the petrochemical industry, aiming to find the shortest smooth inspection path. The problem was modeled as a multiple traveling salesman problem based on Dubins curve. It was achieved by using Dubins curve and the rolling branch-and-bound algorithm. To achieve the optimal inspection path planning, the rolling branch-and-bound algorithm was proposed to update the path length constantly, and the optimal path was sought by continuous iterative optimization of the upper and lower bounds. Besides, the algorithm combined the minimum insertion algorithm with the greedy algorithm to obtain better candidate solutions to prune more branches and optimize the inspection path. And then, the smooth Dubins path was planned by discretizing the heading angle of each grid cell and using the sliding window. Simulation results demonstrate that the proposed algorithm has better performance in terms of exploration time compared to other existing inspection path planning algorithms.