To explore the signal recovery of a noisy image after compressed sensing, a signal recovery model was established to solve the noise problems in engineering applications. As traditional greedy algorithm can not recover the signals added into noise after compressed sensing, this paper proposes an iterative shrinkage-thresholding method to implement the signal recovery. Details of this algorithm were analyzed, and the signal recovery of noise after compressed sensing which contains Gaussian noise and 10% impulse noise, 5% impulse noise was simulated. Then, it was compared with the Orthogonal Matching Pursuit(OMP) and the Parallel Coordinate Descent (PCD) algorithms. Simulation results show that this proposed method completely recovers noise-free sparse signal. It has a strong robustness for recovering signal with noise after compressed sensing, and the recovery error occurs mainly at the peak .It is also worth mentioning that increasing the number of measurement rows and iterations is able to enhance the anti-noise performance of this method. The result also indicates that this algorithm shows excellent characteristics when the Gaussian noise and low-desity impulse noise are processed, but has no many advantages while dealing with high-density impulse noise.