Aiming at the disadvantages of slow convergence of standard grey wolf optimizer (GWO) and easy to fall into local optimality, an improved grey wolf optimizer (IGWO) with improved iterative local search is proposed. First, the uniformity and diversity of the initial population were enhanced by the strategy of the best point set. Secondly, the dual convergence factor is used, which is nonlinear and adaptive updating based on population location, to balance the global exploration and local development ability in the whole period of population optimization. Thirdly, European dynamic weight and Levy flight strategy were introduced into the population position updating formula to improve the optimization accuracy and help the population jump out of the local optimal value. Finally, the improved iterative local search is introduced to make the search ability of the algorithm more flexible and help the algorithm accelerate convergence. Through the simulation analysis of 10 benchmark test functions and the comparison of population optimization balance, it is proved that IGWO has better optimization accuracy, stability and convergence speed. Then IGWO was applied to the engineering optimization problem. Compared with GWO, GJO, WOA, HSSAHHO, SCHOA, NCPGWO, DSFGWO 7 algorithms, the fitness was optimized by 3.25%, 27.2%, 28.9%, 3.15%, 3.04%, 2.33%, 0.07%, respectively. The feasibility and effectiveness in engineering application are proved.