The grey wolf optimizer is an effective and well-known meta-heuristic algorithm, but it also has the weaknesses of insufficient population diversity, falling into local optimal solutions easily, and unsatisfactory convergence speed. Therefore, we propose a hybrid grey wolf optimizer (HGWO), based mainly on the exploitation phase of the harris hawk optimization. It also includes population initialization with Latin hypercube sampling, a nonlinear convergence factor with local perturbations, some extended exploration strategies. In HGWO, the grey wolves can have harris hawks-like flight capabilities during position updates, which greatly expands the search range and improves global searchability. By incorporating a greedy algorithm, grey wolves will relocate only if the new location is superior to the current one. This paper assesses the performance of the hybrid grey wolf optimizer (HGWO) by comparing it with other heuristic algorithms and enhanced schemes of the grey wolf optimizer. The evaluation is conducted using 23 classical benchmark test functions and CEC2020. The experimental results reveal that the HGWO algorithm performs well in terms of its global exploration ability, local exploitation ability, convergence speed, and convergence accuracy. Additionally, the enhanced algorithm demonstrates considerable advantages in solving engineering problems, thus substantiating its effectiveness and applicability.