In this study, an image denoising method for the synthetic aperture radar (SAR) images is proposed. When reconstructed from low-sampling-rate measurements using a compressed sensing (CS) based method, the reconstructions still suffer from noise and aliasing for the sampling rate is much lower than the Nyquist sampling rate (15%-25%). To in future improve the reconstruction, we proposed an imaging denoising method for CS-based reconstructed SAR image. In this proposed denoising method, the pending SAR image is treated as a level set function. We design a step curvature flow function using which the aliasing and noise are eliminated and the clarity of objects of interest in the SAR images are enhanced. Simulation and experimental results illustrated that only a 20% measurement is necessary in the SAR experiment to identify the objects of interest with the proposed method.