Abstract: An adaptive fast recovery algorithm (AFast) is proposed to solve the problem of poor reconstruction performance for compressed sensing of noisy speech with low signal to noise ratio. This method combines row echelon measurement matrix and a new fast recovery algorithm, and adaptively selects the optimal reconstruction parameters according to the signal to noise ratio of noisy speech signal and enhances the signal to noise ratio while reconstructing the speech. The adaptive fast recovery algorithm is simple and fast and does not require pre-calculated signal sparsity. Simulation experiment results demonstrate that the proposed algorithm outperforms basis pursuit algorithm and adaptive conjugate gradient projection algorithm and fast reconstruction algorithm, and the adaptive fast recovery algorithm is faster than basis pursuit algorithm and adaptive conjugate gradient projection algorithm, but slightly slower than fast recovery algorithm.