In this paper, we propose the shared mixture GMM classifier. Mixtures of a GMM which represent areas in the feature space must have very less overlap across classes for best performance. If not, patterns of a class belonging to regions of overlap score high likelihoods with not only the mixture of its own class, but also that mixture of another class thereby making a high contribution to the likelihood score with respect to the other class model. We propose a computational method of determining if such mixtures exist and using an automatic method of determining such mixtures based on discriminability between classes, we propose choosing the mixtures for each GMM from the set of all mixtures of all GMMs. Mixtures that have significant overlap with other classes get shared between the contending classes. Weights are based on cluster-class membership matrix defined in the paper. We have compared the performance of this shared mixture GMM with a conventional GMM, for a 14 class music instrument recognition task. The new model performs competitively compared to the conventional GMM, and outperforms it when there is lesser training data.