Abstract: The compressed sensing (CS) sparse signal recovery is actually solving a system of underdetermined linear equations within the sparse nature of its solution. The compressed sampling matching pursuit (CoSaMP) algorithm directly selects support sets of twice nonzero elements number from the maximizing signal proxy without a quality criterion for every iterative time. The stepwise compressed sampling matching pursuit (SWCoSaMP) algorithm is proposed in this paper, which uses the iterative method to obtain the sparse signal support set. It acquires the sparse signal support set by the definition of the block matrix inversion so that reconstructs the sparse signal. The recovery error’s L-2 norm is also given corresponding with the support set for every iterative time. Compared with CoSaMP, simulative results show that the new algorithm has a good recovery performance for the sparse signal whose nonzero values are distributed uniform or Gaussian.