Inspired by the fact that normalized graph Laplacian is superior to the non-normalized one in spectral clustering, in this paper we develop a new symmetric matrix called normalized modularity matrix which has different properties with the normalized graph Laplacian. And thus a new spectral clustering algorithm is derived based on this new matrix. Experimental results show the performance of the proposed algorithm: (1) being helpful in detecting intrinsic cluster number, (2) being competitive to two baseline algorithms.