In this paper, a speech endpoint detection algorithm is proposed. The proposed algorithm is a kind of state transition-based ones for speech detection. To reject short-duration acoustic pulses which can be considered noises, it utilizes duration information of all detected pulses. For the optimization of parameters related with pulse lengths and energy threshold to detect speech intervals, an exhaustive search scheme is adopted while speech recognition rates are used as its performance index. Experimental results show that the proposed algorithm outperforms the baseline state-based endpoint detection algorithm. At 5 dB input SNR for the beamforming input, the word recognition accuracies of its outputs were 78.5% for human voice noises and 81.1% for music noises.