Gaussian mixture models (GMM) have been widely and successfully used in speaker recognition during the last decades. They are generally trained using the generative criterion of maximum likelihood estimation. In an earlier work, we proposed an algorithm for discriminative training of GMM with diagonal covariances under a large margin criterion. In this paper, we present a new version of this algorithm which has the major advantage of being computationally highly efficient. The resulting algorithm is thus well suited to handle large scale databases. We carry out experiments on a speaker identification task using NIST-SRE'2006 data and compare our new algorithm to the baseline generative GMM using different GMM sizes. The results show that our system significantly outperforms the baseline GMM in all configurations, and with high computational efficiency.