Due to the fact that the sparsity adaptive matching pursuit(SAMP) algorithm has the disadvantages of overmuch candidate atoms, overlong reconstruction time and fixed selection of pace, the paper proposes a modification algorithm based on SAMP. Firstly, by combining the sparse degree of preset values with excessive estimate criterion, this algorithm conducts rapid estimation of real sparse degree. Then the fuzzy threshold method is used to improve the accuracy of candidate atoms. Finally, the iteration stop condition is improved through utilizing atoms relative threshold so as to realize accurate reconstruction of signals. The simulation experiments verify that, compared with the SAMP algorithm, the proposed algorithm not only has higher speed of signal reconstruction, but also improves the quality of reconstruction.