Gaussian mixture models (GMM), trained using the generative cri- terion of maximum likelihood estimation, have been the most popular ap- proach in speaker recognition during the last decades. This approach is also widely used in many other classi cation tasks and applications. Generative learning in not however the optimal way to address classi cation problems. In this paper we rst present a new algorithm for discriminative learning of diagonal GMM under a large margin criterion. This algorithm has the ma- jor advantage of being highly e cient, which allow fast discriminative GMM training using large scale databases. We then evaluate its performances on a full NIST speaker veri cation task using NIST-SRE'2006 data. In particular, we use the popular Symmetrical Factor Analysis (SFA) for session variability compensation. The results show that our system outperforms the state-of-the- art approaches of GMM-SFA and the SVM-based one, GSL-NAP. Relative reductions of the Equal Error Rate of about 9.33% and 14.88% are respec- tively achieved over these systems.