Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity basis. In this paper, we propose a new framework for compressed sensing recovery problem using iterative approximation method via L0 minimization. Instead of directly solving the unconstrained L0 norm optimization problem, we use the linearization and proximal points techniques to approximate the penalty function at each iteration. The proposed algorithm is very simple, efficient, and proved to be convergent. Numerical simulation demonstrates our conclusions and indicates that the algorithm can improve the reconstruction quality.