Aiming at the shortcomings of the traditional sparrow search algorithm (SSA) in path planning, such as its high time-consumption, long path length, it being easy to collide with static obstacles and its inability to avoid dynamic obstacles, this paper proposes a new improved SSA based on multi-strategies. Firstly, Cauchy reverse learning was used to initialize the sparrow population to avoid a premature convergence of the algorithm. Secondly, the sine–cosine algorithm was used to update the producers’ position of the sparrow population and balance the global search and local exploration capabilities of the algorithm. Then, a Lévy flight strategy was used to update the scroungers’ position to avoid the algorithm falling into the local optimum. Finally, the improved SSA and dynamic window approach (DWA) were combined to enhance the local obstacle avoidance ability of the algorithm. The proposed novel algorithm is named ISSA-DWA. Compared with the traditional SSA, the path length, path turning times and execution time planned by the ISSA-DWA are reduced by 13.42%, 63.02% and 51.35%, respectively, and the path smoothness is improved by 62.29%. The experimental results show that the ISSA-DWA proposed in this paper can not only solve the shortcomings of the SSA but can also plan a highly smooth path safely and efficiently in the complex dynamic obstacle environment.