Most of the existing influence maximization problem in social networks only focus on single relationship social networks, that is, there is only one relationship in social networks. However, in reality, there are often many relationships among users of social networks, and these relationships jointly affect the propagation of network information and its final scope of influence. Based on the classical linear threshold model and combined with various relationships between network nodes, in this paper MRSN-LT propagation model is proposed to model the influence propagation process between nodes in multiple relationships social networks. Then, MRSN-RRset algorithm based on reverse reachable set is proposed to solve the problem of low computational performance caused by greedy algorithm in the research process of traditional influence maximization. Finally, the experimental results on real data sets show that the proposed method has better influence propagation scope and greater computational performance improvement.