To tackle the problems of poor convergence accuracy and proneness to falling into local optima in the standard Harris Hawk Optimization (HHO) algorithm, we put forward an improved version that integrates iterative chaotic mapping and Lévy random walk strategies. Firstly, iterative mapping is utilized to initialize the Harris hawk population, thus guaranteeing population diversity. For the global search phase, Lévy random walk is adopted to boost the algorithm’s global optimization ability, while also strengthening its local exploitation performance. In this study, the proposed algorithm is tested with 12 test functions from the CEC2022 suite, with comparisons made against the standard HHO algorithm and the HHO variant improved by combining Cauchy mutation and Circle chaotic mapping. The results indicate that the improved algorithm achieves notably enhanced convergence speed and optimization performance.