The standard salp swarm algorithm (SSA) has low convergence accuracy and slow convergence speed. In order to solve these problems, a salp swarm algorithm based on adaptive inertia weight (AIWSSA) is proposed. Firstly, the inertia weight factor is introduced into the follower position update formula to evaluate the degree of influence between the individuals. Secondly, the combination of population successful rate and nonlinear decreasing function is applied to adjust the inertia weight factor adaptively to balance the exploration and exploitation abilities of the proposed algorithm. Finally, the differential mutation for the non-optimal individuals is used to avoid the algorithm of being trapped into local optimum. Then the experiments on the 12 benchmark test functions are conducted. The results show that the proposed AIWSSA has higher convergence accuracy, convergence speed and robustness, and the Wilcoxon statistical test results demonstrate that it has better performance compared with the standard salp swarm algorithm, the improved salp swarm algorithms and other swarm intelligence algorithms. Two constrained engineering design problems are applied to verify the effectiveness of the algorithm.