In speaker identification, most of the computation is due to the distance or likelihood calculation between feature vectors of the test signal and the speaker model in the database. The time required for identifying a speaker is a function of feature vectors and their dimensionality and the number of speakers in the database. In this paper, we focus on optimizing the performance of Gaussian mixture (GMM) based speaker identification system. An improved approach for model parameter calculation is presented. The advantage of proposed approach lies in the reduction in computational time by a significant amount over an approach which uses expectation maximization (EM) algorithm to calculate the model parameter values. This approach is based on forming clusters and assigning weights to them depending upon the number of mixtures used for modeling the speaker. The reduction in computation time depends upon how many mixtures are used for training the speaker model.