The GMM-UBM framework has been proved to be one of the most effective approaches to the automatic speaker verification (ASV) task in recent years. In this letter, we first propose an approximate decision function of traditional GMM-UBM, from which it is shown that the contribution to classification of each Gaussian component is equally important. However, research in speaker perception shows that a different speech sound unit defined by Gaussian component makes a different contribution to speaker verification. This motivates us to emphasize some sound units which have discriminability between speakers while de-emphasize the speech sound units which contain little information for speaker verification. Experiments on 2006 NIST SRE core task show that the proposed approach outperforms traditional GMM-UBM approach in classification accuracy.