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A method for synthetic aperture radar (SAR) imaging using maximum a posteriori (MAP) estimation based on multiplicative speckle model is presented. The new method uses the total variation (TV) minimization to regularize the solution. The reconstruction of SAR image is formulated as a biconvex optimization problem, which is solved by the alternate convex search (ACS) method. Experiments on Radarsat-1 raw data show that the proposed method can recover most of the structural and texture details of the imaged scene using only a half of raw data. Compared with regular regularization methods for SAR imaging with incomplete data, the proposed method performs much better on less sparse scenes.