The smoothed l0 norm algorithm in compressive sensing introduces smoothed functions to approximate the l0 norm. The problem of minimization of l0 norm can be transferred to a convex optimization problem of the smoothed functions, which could be used efficiently for compressive sensing reconstruction. Aiming at the choice of appropriate smoothed functions and improvement of the robustness of the algorithm, a new smoothed function sequence with gradient projection method has been proposed to solve the optimization problem in this paper. Singular value decomposition (SVD) method has been further proposed to improve the robustness of algorithm,then the accurate reconstruction of sparse signal is realized.Experimental results show that the proposed algorithm improve ignificantly in both the reconstruction accuracy and the peak value signal -to-noise ratio under the same test conditions.