The hippopotamus optimization algorithm (HO) is a novel metaheuristic algorithm that solves optimization problems by simulating the behavior of hippopotamuses. However, the traditional HO algorithm may encounter performance degradation and fall into local optima when dealing with complex global optimization and engineering design problems. In order to solve these problems, this paper proposes a modified hippopotamus optimization algorithm (MHO) to enhance the convergence speed and solution accuracy of the HO algorithm by introducing a sine chaotic map to initialize the population, changing the convergence factor in the growth mechanism, and incorporating the small-hole imaging reverse learning strategy. The MHO algorithm is tested on 23 benchmark functions and successfully solves three engineering design problems. According to the experimental data, the MHO algorithm obtains optimal performance on 13 of these functions and three design problems, exits the local optimum faster, and has better ordering and stability than the other nine metaheuristics. This study proposes the MHO algorithm, which offers fresh insights into practical engineering problems and parameter optimization.