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This paper proposed an overlapping community discovery method based on cored nodes and the Latent Allocation Dirichlet (LDA) topic modeling, which is called as CN-LDA. CN-LDA models the complex network with the LDA model, finds the probability of each edge in each community, and then uses statistical methods to calculate the probability value of each node in each community. Furthermore, to determine the community number of the network, we give an algorithm to identify the core nodes of the complex networks with the threshold random walk. CN-LDA also can be used to determine overlapping nodes. We do experiments to Compare CN-LDA with some other community algorithms in several real-world social networks. The experimental results showed that CN-LDA is effective to discover overlapping communities.