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. To show the effectiveness of the new algorithm, we carry out a full NIST speaker verification task using NIST-SRE'2006 data. The results show that our system outperforms the baseline GMM, and with high computational efficiency.