In order to overcome the shortcomings of traditional algorithms such as depending on the selection of initial value, the non-complete number of solutions and the poor solution accuracy, a gray wolf optimization algorithm combined with pathfinder algorithm (PGWO) is proposed. Due to the slow convergence speed of the gray wolf optimization algorithm, this paper combines the pathfinder algorithm to modify the position of an individual gray wolf according to the update mechanism of the follower in the pathfinder algorithm, so as to balance the global search and local search abilities of the algorithm. Finally, the simulation results of nine groups of multi-roots nonlinear equations are compared with other swarm intelligent algorithms. The experimental results show that the PGWO method improves the solution accuracy of multi-roots nonlinear equations, and the number of solutions is significantly improved, which further proves the effectiveness of the proposed algorithm.