In the mobile robot path planning problem in static multi-obstacle environment, Particle Swarm Optimization (PSO) algorithm has the disadvantages of easy premature convergence and poor local optimization ability, resulting in low accuracy of robot path planning. To solve the problem, a Multi-Objective Grasshopper Optimization Algorithm (MOGOA) was proposed. The path length, smoothness and security were taken as path optimization targets according to the mobile robot path planning requirements, and the corresponding mathematical model of multi-objective optimization problem was established. In the process of population search, the curve adaptive strategy was introduced to speed up the convergence of the algorithm, and the Pareto optimal criterion was used to solve the coexistence problem of the above three targets. Experimental results show that the proposed algorithm finds shorter paths and shows better convergence while solving the above problems. Compared with the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, the proposed algorithm has the path length reduced by about 2.01 percentage, and the number of iterations reduced by about 19.34 percentage.