Abstract: In this paper spectral clustering was applied to detect the community in social network, and a new method was proposed to estimate the number of communities. According to this new method, the number of communities was estimated by calculating and analyzing the eigenvalues distribution of Laplacian matrix. K-means algorithm was used to clustering vector space which was constructed by eigenvectors of Laplacian matrix. The method was tested on a range of examples, including real-world and synthetic networks. Experimental results show that the method for community detection is accurate and effective.