Synthetic Aperture Radar (SAR) images can be reconstructed by using random undersampled data.The smoothed l0 norm (SL0) method is a compressed sensing SAR image reconstruction method with fast reconstruction speed and a simple algorithm.However,the steepest descent technique used in the method may result in the phenomenon of contour jaggies in the iteration direction,which greatly increases the time consumption of SAR image reconstruction.In addition,the Gaussian fitting function that is used in the method has a poor matching degree to the discrete l0 norm,which will affect the accuracy of image reconstruction,and the resolution of the reconstructed SAR image is not high enough.To solve the above problems,an SAR image reconstruction method based on Almost-Hybird Newton Smoothed l0 norm (A-HNSL0) is proposed by introducing the approximate hyperbolic tangent function and the hybrid optimization algorithm.Experimental results show that the proposed method makes certain improvements to both the reconstruction speed and the reconstruction accuracy under the same external conditions.