To develop a more robust endpoint detection algorithm, this paper first proposes a fuzzy adaptive smoothing algorithm. The general idea underlying adaptive smoothing is to adapt the short-term sub-band mean of the amplitude to the local attributes of speech on the basis of discontinuity measures. The adaptive smoothing algorithm in this paper utilizes a scale-space framework through the minimal description length (MDL). We recommend using the fuzzy multi-attribute decision making approach to select the proper sub-bands where the word boundary can be more reliably detected. The process and simulation of the fuzzy adaptive smoothing algorithm are given. The parameters utilize the mean amplitude of the audible frequency range (300 - 3 700 Hz)and the sub-band mean of the amplitude ( 16 band filter-bank). We selected the audible band energy because of its usefulness in detecting high-energy regions and making the distinction between speech and noise. Otherwise, the fuzzy adaptive smoothing algorithm is processed in sub-band speech to utilize the full range of frequency information.