An adaptive total variation method to reduce speckles with preservation of targets in synthetic aperture radar (SAR) images is investigated. Based on the gamma distribution of speckle, an adaptive total variational model is proposed with its fidelity term derived from a framework of weighted maximum likelihood estimation and its regularity term with constraints on the gradient of an image. It has merits of preserving textures and targets since the a priori distribution of noise is incorporated into the model and the weights are essentially image data driven, which can adaptively adjust the weights. The mathematical analysis is carried out, and proof of existence and uniqueness of a solution for the corresponding function is also presented. Theoretical analysis and experiments on both the simulated and real SAR images demonstrate that the method proposed here performs favorably.