This paper proposed the shortest smooth path planning algorithm of multiple UAVs in the petrochemical industry. It is achieved by using Dubins curve and the rolling branch-and-bound algorithm. The algorithm describes the multi-UAV inspection path planning problem as a multiple travelling salesman problem based on Dubins. To achieve the optimal inspection path planning, the rolling branch-and-bound algorithm is adopted to update the path length constantly, and the optimal path is sought by continuous iterative optimization of the upper and lower bounds. Besides, it combines 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 is 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.