Conventional speaker recognition systems use the Universal Background Model (UBM) as an imposter for all speakers. In this paper, speaker models are clustered to obtain better imposter model representations for speaker verification purpose. First, a UBM is trained, and speaker models are adapted from the UBM. Then, the k-means algorithm with the Euclidean distance measure is applied to the speaker models. The speakers are divided into two, three, four, and five clusters. The resulting cluster centers are used as background models of their respective speakers. Experiments showed that the proposed method consistently produced lower Equal Error Rates (EER) than the conventional UBM approach for 3, 10, and 30 seconds long test utterances, and also for channel mismatch conditions. The proposed method is also compared with the i-vector approach. The three-cluster model achieved the best performance with a 12.4% relative EER reduction in average, compared to the i-vector method. Statistical significance of the results are also given.