In this paper, a method that uses the wavelet transform to suppress the speckle noise in synthetic aperture radar (SAR) images is described. Based on the previous wavelet approach, the properties of the wavelet coefficients have been taken into more account so that the edges information in images can be preserved well and the computational burden has been reduced at the same time. And this method is also compared with other classical denoising methods, such as median filter, Lee filter, Frost filter and so on. The results of the simulations and application to synthetic image and real SAR images prove the good performance of proposed new wavelet method.