The Grey Wolf Optimization Algorithm (GWO) is an algorithm that replicates the leadership and foraging mechanisms of the natural grey wolf, which excels at solving problems in a variety of domains. However, the algorithm tends to converge on local optimal and has a slow convergence rate. This paper proposes an enhanced Grey Wolf optimization algorithm (HTGWO) based on hyperbolic tangent inertia weights to solve this problem. HTGWO employs inertia weight based on hyperbolic tangent functions to balance GWO’s global and local search capabilities. HTGWO has a quicker convergence rate and more accurate solutions than GWO. Five classical test functions construct comparative experiments between HWGWO and five classical intelligent optimization algorithms. The comparison results indicate that HWGWO has superior convergence speed, solution precision, and stability compared to the other five classical intelligent optimization algorithms. Moreover, experimental evidence suggests that HWGWO is more effective at solving multi-modal than uni-modal functions.