Aiming at the low precision and local optima stagnation of the grey wolf optimization (GWO) algorithm in dealing with complex optimization problems, a grey wolf optimization algorithm based on strengthening the hierarchy of wolves(GWOSH) is proposed. The new algorithm provides two kinds of hunting-modes which are following hunting mode and self-exploration mode for each grey wolf, and each grey wolf chooses its hunting-mode according to the social hierarchy of their own. In the following hunting mode, the grey wolf only depends on the position of higher level wolves to guide itself to search the optimal area. In the self-exploration mode, the individuals will examine the location of the higher level grey wolf and its position at the same time, and judge the position of prey independently based on these information. In the two hunting-modes, a survival of the fittest selection rule is introduced to ensure the evolutionary direction of the population. The optimization results on 12 benchmark functions show that GWOSH has stronger global searching ability and is more effective in the premature convergence avoidance and more suitable for solving high-dimensional complex optimization problems compared with the available algorithms.