The traditional Harris Hawks optimization algorithm is prone to the local shortest path, slow search speed and poor path accuracy in indoor mobile robot path planning. For the above problems, a multi-strategy improvement of the Harris Hawks optimization algorithm (MIHHO) is proposed. In this study, a Chebyshev chaotic mapping strategy is used to increase the diversity of the Harris Hawk population, improve the global search performance of the Harris Hawk algorithm, and prevent being trapped in the locally optimal path. A fusion exploration mechanism is proposed to fuse the discovery mechanism of the sparrow algorithm with the exploration mechanism of the HHO. Then the influence factor E is improved to improve the algorithm’s search accuracy and search efficiency, and finally, in the design of a dynamic Lévy flight strategy, which accelerates the convergence speed of the algorithm and improves the robot planning speed. Simulation results show that the proposed MIHHO method exhibits better search performance in path planning, improved planning efficiency, and superior quality of planned paths.