Abstract: Based on the approximate sparsity of speech signal in discrete cosine basis, Compressed Sensing theory is applied to compress and decompress speech signal in this paper, that is, speech signal is projected to a sparse random measurement matrix and reconstructed by Linear Program. Features of compressed sensing measurements of speech signal is researched in this paper. According to the decentralization characteristic of amplitude spectrum distribution of compressed sensing measurements of speech signal and difference of amplitude spectrum of compressed sensing measurements of voice and non-voice speech, endpoint detection algorithm based on cepstral distance of compressed sensing measurements of speech signal is proposed. Simulation with noisy speech signals ranging from 4dB to 20 dB is made. The simulation results show that endpoint detection algorithm based on cepstral distance of compressed sensing measurements can achieve the same performance of cepstral distance of speech signal sampled by Nyquist Theory in noisy circumstance. The amount of calculation of endpoint detection of speech is reduced by the compressed sensing technology.