To overcome the problems that the iterative number of compressive sampling matching pursuit(CoSaMP) algorithm is heavily dependence on sparsity K, and the larger redundancy of the candidate atoms leads to low precision, a modified CoSaMP algorithm is proposed. The algorithm reconstructs images by using fuzzy threshold to select candidate atoms for supporting set and setting the correlation threshold between measure matrix and residual error as the condition for stopping iteration. The simulations demonstrate that the modified algorithm spends less computing time than the CoSaMP algorithm, and improves the performance of the recovery.