The swarm intelligence algorithm is a new technology proposed by researchers inspired by the biological behavior of nature, which has been practically applied in various fields. As a kind of swarm intelligence algorithm, the newly proposed sparrow search algorithm has attracted extensive attention due to its strong optimization ability. Aiming at the problem that it is easy to fall into local optimum, this paper proposes an improved sparrow search algorithm (IHSSA) that combines infinitely folded iterative chaotic mapping (ICMIC) and hybrid reverse learning strategy. In the population initialization stage, the improved ICMIC strategy is combined to increase the distribution breadth of the population and improve the quality of the initial solution. In the finder update stage, a reverse learning strategy based on the lens imaging principle is utilized to update the group of discoverers with high fitness, while the generalized reverse learning strategy is used to update the current global worst solution in the joiner update stage. To balance exploration and exploitation capabilities, crossover strategy is joined to update scout positions. 14 common test functions are selected for experiments, and the Wilcoxon rank sum test method is achieved to verify the effect of the algorithm, which proves that IHSSA has higher accuracy and better convergence performance to obtain solutions than 9 algorithms such as WOA, GWO, PSO, TLBO, and SSA variants. Finally, the IHSSA algorithm is applied to three constrained engineering optimization problems, and satisfactory results are held, which proves the effectiveness and feasibility of the improved algorithm.