Abstract: Compressive sensing is a novel signal sampling and processing theory under the condition that the signal is sparse or compressible. In this paper, a new Modified Sparsity Adaptive Matching Pursuit (MSAMP) Algorithm is proposed for signal reconstruction without prior information of the sparsity. Firstly, a new sparsity estimation method based on atom matching test is used to get an initial estimation of sparsity. Then it realized the close approach of signal sparse step by step under the frame of sparsity Adaptive Matching Pursuit (SAMP). But the step size in MSAMP algorithm is variable rather than the fixed one in SAMP algorithm. At the beginning of step iterations, high value of step size, causing fast convergence of the algorithm is used initially to realise the coarse approach of signal sparse, and in the later step iterations smaller value of step size, advancing the performance of the algorithm is used to achieve the precise approach of signal sparse. Finally, it realized the precise reconstruction of sparse signal. The analytical theory and simulation results show that significant reconstruction performance improvement is achieved. The problem of over or under estimation in SAMP algorithm under the condition of large sparsity is almost resolved. Also, the convergence of the algorithm is much faster than the fixed step size algorithm.