Harris hawks optimization (HHO) algorithm is one of the newly population-based optimization algorithms. However, when solving complex problems, HHO still suffers from certain limitations, such as premature convergence and suboptimal solution accuracy. To overcome these shortcomings, a new and enhanced version of HHO is proposed, named the hybrid strategy Harris hawks optimization (HSHHO) algorithm. Firstly, the exploration strategy based on SPM chaotic map and variable logarithmic spiral is proposed to enhance the exploration capability of HHO. Lastly, the Cauchy-Gaussian-based elite perturbation strategy is proposed to amplify the local search ability of the algorithm and improve solution accuracy. To evaluate the performance of HSHHO, comprehensive experiments are conducted on 23 test functions. The experimental results demonstrate that performance of HSHHO is significantly better than other metaheuristic optimization algorithms. Additionally, HSHHO and six well-known optimization algorithms are validated on eighteen feature selection problems, and the experimental results reveal that HSHHO achieves superior performance in terms of fitness and classification accuracy.