Abstract: This paper proposed an improved OMP(Orthogonal Matching Pursuit)algorithm that replaced Ordinary Least Square algorithm with Conjugate Gradient Descent algorithm based on the backfitting idea of Subspace Pursuit algorithm,in order to solve the problem of contradiction between reconstruction effort and time required of OMP algorithm under compressive sensing theory.This paper also made simulation experiment on the accuracy and stability of reconstruction of the improved algorithm.The result showed that the improved algorithm made the quality of reconstruction satisfying with better speed and stability of reconstruction.