The grey wolf optimization algorithm is an efficient optimization technology, however, it still has some shortcomings, such as low accuracy, slow convergence speed and easy to fall into local optimum. Therefore, a modified grey wolf optimization algorithm (MGWO) was proposed. Three improved strategies were introduced into the algorithm: the strategy of the convergence factor adjustment with exponential law, the adaptive position updating strategy of grey wolf and the revised dynamic weight strategy. Through the implementation of two groups of comparative experiments on 10 benchmark functions, the effectiveness of the three improved strategies was verified. The experimental results show that the MGWO-4 with the three improved strategies improves the performance of the basic grey wolf optimization algorithm (GWO) significantly, and is superior to the improved grey wolf algorithm and several other optimization algorithms in other literatures. The experimental results on an engineering design question further prove that MGWO is a powerful optimization technique.