The multi-robot systems (MRS) task planning model is established by the similar Multiple Traveling Salesman Problem (SMTSP) in this paper. An improved Genetic Algorithm (GA) is proposed to optimize the task planning under different objectives. Compared with the traditional algorithm, the main contribution of this paper is the elite set strategy of genetic operation which improves the optimization. Through the simulation analysis, the improved algorithm gets faster convergence and retains the diversity of the population by swapping, sliding and flipping evolutionary operation of the elite set. A tunable weight parameter is adopted to optimize the total distance and the maximum completion time of the task planning and finally the best solution with balanced path and less energy consumption is obtained. The MRS task planning optimization method proposed in this paper has wide utilization prospects, such as logistics and distribution, space scheduling, battlefield distribution.