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 random Gauss measurement matrix and reconstructed by Linear Program， the relationship between reconstruction error and  numbers of measurement vector is studied，also，the vary of spectrum of reconstruction signal is analysed. According to the less vary of spectrum of Compressed Sensing reconstruction signal than original signal in noise conditions， a method based  on Compressed Sensing reconstruction signal to prove the performance of Speaker Recognition system in noise conditions is proposed. The opitimal numbers of measurement vector are given to achieve the highest recognition accuracy in different SNR conditions.