Discrimination between speech and music is important in many multimedia applications. In this paper, focusing on the spectral change characteristics of speech and music, we propose a new method of speech/music discrimination based on cepstral distance. Instead of using cepstral distance between the frames with fixed interval, the minimum of cepstral distances among neighbor frames is employed to increase discriminability between fast changing music and speech. And, to prevent misclassification of speech segments including short pause into music, short pause segments are excluded from computing cepstral distance. The experimental results show that proposed method yields the error rate reduction of$68\%$, in comparison with the conventional approach using cepstral distance.