This paper studies the effects of the method, CMS(Cepstral Mean Subtraction), (which compensates for some of the speech distortion. caused by telephone channels), on the performance of the text-dependent speaker identification system. This system is based on the VQ(Vector Quantization) and HMM(Hidden Markov Model) method and chooses the LPC-Cepstrum and Mel-Cepstrum as the feature vectors extracted from the speech data transmitted through telephone channels. Accordingly, we can compare the correct recognition rates of the speaker identification system between the use of LPC-Cepstrum and Mel-Cepstrum. Finally, from the experiment results table, it is found that the Mel-Cepstrum parameter is proven to be superior to the LPC-Cepstrum and that recognition performance improves by about 10% when compensating for telephone channel using the CMS.