The grey wolf optimizer (GWO) algorithm proposed recently has strong local search ability and fast convergence, but it has some defects, such as poor global search ability in solving high-dimensional functions and complex optimization problems.Therefore, this paper proposes an improved GWO, namely GWO with opposition- learning and differential mutation (ODGWO). Firstly, a max-min opposition learning strategy and a dynamical and random differential mutation operator are proposed, which are integrated with GWO to enhance its global search ability. Then, in order to balance exploration and exploitation well to improve the overall performance, one-dimensional operation and full-dimensional operation are applied to the first half and the latter one of the search phase respectively to form the ODGWO consequently. Finally, the ODGWO is used for the high-dimensional function and fuzzy C-means (FCM) clustering optimization.The experimental results on many high-dimensional (30, 50 and 1000 dimension) benchmark functions show that the ODGWO has significantly higher global search ability than the GWO does, and the ODGWO outperforms the state-of-the-art algorithms.As for FCM optimization on seven standard datasets, the ODGWO shows better clustering optimization performance compared with the GWO, the GWOepd and the LGWO, and it will be applied to more real-world optimization problems.