The salp swarm algorithm imitates the swarm behavior of salps during navigation and hunting that has been proven the superiority of search for best solution. However, although it has sufficient global search ability, it is still worth paying attention to problems of falling into local optima and lower convergence accuracy. This paper proposes some improvements to the salp swarm algorithm that are based on a nonlinear dynamic weight and the mapping mutation operation. Firstly, the nonlinear dynamic weight is helpful for further optimizing the transition from exploration to exploitation and alleviating the local optima stagnation phenomena. Secondly, utilizing a mapping mutation operation can increase the diversity of followers in algorithm, to avoid getting trapped into the local optima during the search and provide a better optimal solution. The proposed algorithm is characterized by a stronger global optimization capability and high convergence accuracy. Finally, to confirm the effectiveness of the proposed algorithm, comparative experiments based on other well-known swarm-based algorithms and each improvement for the original algorithm are conducted. The quantitative results and convergence curves among several algorithms demonstrate that the enhanced algorithm with the nonlinear dynamic weight and mapping mutation operation can outperform the original algorithm.