Classical northern goshawk optimization (NGO) algorithms tends to fall into local optima, slow convergence and insufficient diversity when dealing with multimodal and high-dimensional problems. To address this issue, an improved NGO (INGO) algorithm was proposed. The Lévy flight was introduced to enhance global search capability in exploration phase and prevent fall into local optima. Elite solution guidance and dynamic mutation were designed to boost exploitation ability and convergence efficiency. 18 CEC2017 benchmark functions were selected to test the performance of INGO and other eight optimization algorithms. Additionally, statistical tests were performed by using the Wilcoxon rank sum test and Friedman test. The experimental results reveal that INGO performs well in terms of search precision, convergence speed and robustness. Finally, INGO was applied to solve nonlinear equation systems and two typical engineering optimization problem. The results show that the proposed algorithm can effectively address practical optimization problems.