Aiming at the traditional gray wolf optimization(GWO) algorithm which often encounters the dilemma of local optimum and unsatisfactory convergence efficiency in the mobile robot path planning task, an improved gray wolf optimization(PGWO) algorithm based on Piecewise chaotic mapping is proposed. The PGWO algorithm first initializes the size of gray wolves by using the Piecewise chaotic map to improve the diversity of population distribution. Secondly, the convergence factor $ a $ in the GWO algorithm is adjusted from linear to nonlinear control parameter, and the adjusted convergence factor $ a $ decreases rapidly in the early iteration, which improves the global search ability and avoids falling into local optimum, and gradually decreases in the later iteration to increase the local search ability. Finally, the formula for updating the position of the gray wolf approaching prey in the GWO algorithm is updated by proportional weight based on step Euclidean distance to improve the independent search ability of the gray wolf. In order to verify the performance of the improved algorithm, this paper selects six standard test functions to compare the PGWO algorithm with the GWO algorithm and two different improved gray wolf algorithms. The results show that the PGWO algorithm has good convergence and stability. The PGWO algorithm is applied to three kinds of grid maps with different complexity for global path planning simulation and comparative experiments. The results show that the shortest path of the PGWO algorithm is shortened by 22.09 %, 34.12 % and 47.75 % respectively compared with the GWO algorithm in 20×20, 30×30 and 50×50 grid maps.