The complete influence time (CIT) in a social network is defined as the period of time it takes to influence all the individuals in the network after a cascade of influence is triggered.In many applications, decision makers attempt to minimize the CIT to speed up the process of influence diffusion, however they often encounter the cases where different types of uncertainty coexist.In this paper, we study the problem of minimizing the CIT in a social network under hybrid uncertain environments where randomness and fuzziness coexist.We consider the individual costs as random fuzzy variables and propose three decision models according to different decision criteria in random fuzzy theory.A greedy algorithm with heuristics that can trade off between optimality and complexity is designed for solving the models.Numerical experiments are preformed to illustrate the effectiveness of our algorithm.