Speech processing has emerged as one of the important application area of digital signal processing. The objective of automatic speaker recognition is to extract, characterize and recognize the information about speaker identity. This paper proposes the comparison of the MFCC and the Vector Quantisation technique for speaker recognition. Feature vectors from speech are extracted by using Mel-frequency cepstral coefficients which carry the speaker's identity characteristics and vector quantization technique is implemented through Linde-Buzo-Gray algorithm. Vector quantization uses a codebook to characterize the short-time spectral coefficients of a speaker. These coefficients are used to identify an unknown speaker from a given set of speakers. The effectiveness of these methods is examined from the viewpoint of robustness against utterance variation such as differences in content, temporal variation, and changes in utterance speed.