In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding $k$ seed nodes in a social network to maximize the influence spread. We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input. We design an algorithm that solves this problem with a solution-dependent bound. We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task. Our empirical results show that parameter uncertainty may greatly affect influence maximization performance and prior studies that learned influence probabilities could lead to poor performance in robust influence maximization due to relatively large uncertainty in parameter estimates, and information cascade based adaptive sampling method may be an effective way to improve the robustness of influence maximization.