Due to the special application environment of the power distribution room inspection robot, the traditional heuristic algorithm used for multi-objective point path planning may deteriorate the solution results, thus failing to obtain the globally optimal solution in practical applications. In response to the above issues, this paper proposes a multi-objective point path planning algorithm based on the serial fusion of improved grey wolf optimization and A*. Firstly, the pre-A* algorithm is used in conjunction with the grid distance formula to calculate the grid distance between any two target points. Then, an improved grey wolf algorithm, which has modified the input variable encoding method and convergence factor formula, is adopted to plan the optimal cruise sequence vector for multiple target points. Finally, the path between adjacent target points in the optimal cruise sequence vector is planned in sequence, and the globally closed-loop planning path for multiple target points is finally obtained. The simulation results show that the optimal path length obtained by the improved grey wolf algorithm is reduced by a maximum of 18.1% compared with the traditional grey wolf algorithm. Compared with the traditional single algorithm optimization, the fusion algorithm reduces the traversed grids by 808 and the path length by 76.4%.