Traditional synthetic aperture radar (SAR) imaging methods focus on high-resolution imaging of the observation scene. In the application of specific target imaging and detection, such as threat target search, the priori knowledge of target can be used for better task performance. Therefore, it is highly desirable to improve the image quality of the target. In this paper, we propose a SAR formation method based on the sparse dictionary. Firstly, the sparse dictionary is learned through the SAR images of a specific target via K-SVD method. Then the SAR formation model is established as a sparse reconstruction problem by incorporating the sparse dictionary. Lastly, the problem is solved via Augment Lagrange Multiplier (ALM) method and Alternating Direction Method of Multipliers (ADMM) method. The proposed method is validated by the simulation, and the results show that the proposed method can effectively reconstruct the target.