The synthetic aperture radar (SAR) images are mainly affected by speckle noise. Speckle degrades the features in the image and reduces the ability of a human observer to resolve fine detail, hence despeckling is very much required for SAR images. This paper presents speckle noise reduction in SAR images using a combination of curvelet and fuzzy logic technique to restore speckle-affected images. This method overcomes the limitation of discontinuity in hard threshold and permanent deviation in soft threshold. First, it decomposes noise image into different frequency scales using curvelet transform, and then applies the fuzzy shrinking technique to high-frequency coefficients to restore noise-contaminated coefficients. The proposed method does not use threshold approach only by proper selection of shrinking parameter the speckle in SAR image is suppressed. The experiment is carried out on different resolutions of RISAT-1 SAR images, and results are compared with the existing filtering algorithms in terms of noise mean variance (NMV), mean square difference (MSD), equal number of looks (ENL), noise standard deviation (NSD) and speckle suppression index (SSI). A comparison of the results shows that the proposed technique suppresses noise significantly, preserves the details of the image and improves the visual quality of the image