Aiming at the shortcomings of salp swarm algorithm(SSA) in solving complex optimization problems, such as easy to fall into local optimization and low convergence accuracy, an improved salp swarm algorithm(ISSA) based on hybrid strategy is proposed. Firstly, Sobol sequence is used to initialize the population of Tarpa scabbard, making the initial population more evenly distributed in the solution space, thereby improving the global optimization ability of the algorithm. Secondly, in the leader position update stage, a step size control factor is introduced to automatically adjust the leader's search range according to different optimization periods, effectively balancing the global search and local search of the algorithm. Then, an improved lens imaging strategy is used to map leaders to avoid the algorithm falling into local optimization. In addition, in the follower position update stage, an autonomous selection following mechanism is introduced to improve the blind obedience of the follower to improve the convergence accuracy of the algorithm. Finally, compared with other representative optimization algorithms, simulation experiments are conducted on 12 benchmark test functions, and Wilcoxon rank sum test is conducted. The experimental results show that the ISSA proposed has significant improvement in convergence speed and accuracy, and has better optimization effect and stability compared with other optimization algorithms. In addition, two engineering design case experiments are conducted to further verify the feasibility and applicability of the proposed ISSA.