Based on compressive sensing theory, it aims to solve the problem of sparse signal recovery. On the basis of the analysis of the classical FR conjugate gradient method, a modified FR spectral conjugate gradient method based on the spectral gradient method is proposed. This method combines some characteristics of conjugate parameters of six classical conjugate gradient methods, such as FR,DY， and CD. Additionally, it is proved that the given method has a descending direction and global convergence under the Wolfe line search. Comparing with the numerical results of the other two algorithms, it is shown that the given optimization algorithm has some advantages. The signal reconstruction results show that the proposed method has high signal-to-noise ratio and less time-consuming, and can be effectively applied to the recovery of sparse signals.