Gaussian mixture models (GMM) have been widely and successfully used in speaker recognition during the last decade. However, they are generally trained using the generative criterion of maximum likelihood estimation. In this paper, we propose a simple and efficient discriminative approach to learn GMM with a large margin criterion to solve the classification problem. Our approach is based on a recent work about the Large Margin GMM (LM-GMM) where each class is modeled by a mixture of ellipsoids and which has shown good results in speech recognition. We propose a simplification of the original algorithm and carry out preliminary experiments on a speaker identification task using NIST-SRE'2006 data. We compare the traditional generative GMM approach, the original LM-GMM one and our own version. The results suggest that our algorithm outperforms the two others.