Compressive sensing is a novel theory that can compressively sample and reconstruct signal accurately with high probability.In this paper,firstly,based on statistical analysis of the sparsity of signal,the Laplacian distribution,which has the ability of sparsity description,is used as prior distribution;secondly,using Bayes′ rule,the maximum a posteriori(MAP) estimation of signal can be inferred with measurement vector,Laplacian prior distribution and Gaussian likelihood model;thirdly,the process of MAP estimation is transformed to a minimization problem of reweighted iterative L1 norm.The experimental results show that compared with unweighted L1 norm minimization,the signal reconstruction performance of the new method is improved obviously.The principle and range of choosing the parameters used in the distribution are discussed thoroughly.Compared with classical methods,such as BP and OMP,reconstruction results of the new method are superior with increase of nonzero number of sparse signals.The proposed algorithm is more general and has more profound theoretical meanings than to IRL1.