Compressive sensing (CS) is a novel signal sampling theory under the condition that the signal is sparse or compressible. It has the ability of compressing a signal during the process of sampling. Reconstruction algorithm is one of the key parts in compressive sensing,and it is of great significance to verify the sampling accuracy. In this paper,properties of the existing reconstruction algorithms are firstly analyzed. And then a new variable step size adaptive matching pursuit (VssAMP) algorithm based on greedy pursuit is presented by introducing an idea of variable step size. The proposed algorithm could control the accuracy of reconstruction by both variable step size and double thresholds although the sparsity of a signal is unknown. The experimental results show that the proposed algorithm can get better reconstruction performances and is superior to other algorithms both visually and objectively.