In this study, we introduce a new factor analysis of Laplacian approach to speaker recognition under the support vector machine (SVM) framework. The Laplacian-projected supervector from our proposed Laplacian approach, which finds an embedding that preserves local information by locality preserving projections (LPP), is believed to contain speaker dependent information. The proposed method was compared with the state-of-the-art total variability approach on 2010 National Institute of Standards and Technology (NIST) Speaker Recognition Evaluation (SRE) corpus. According to the compared results, our proposed method is effective.