The speaker recognition task falls under the general problem of pattern classification. Speaker recognition as a pattern classification problem, its ultimate objective is design of a system that classifies the vector of features in different classes by partitioning the feature space into optimal speaker discriminative space. Linear Discriminant Analysis (LDA) is a feature extraction method that provides a linear transformation of n-dimensional feature vectors (or samples) into mdimensional space (m < n), so that samples belonging to the same class are close together but samples from different classes are far apart from each other. In this paper we discuss the issue of the application of LDA to our Gaussian Mixture Model (GMM) based speaker identification task. Applying LDA improved the identification performance.