In order to achieve simultaneously excellent multiple moving target imaging quality and imaging efficiency, a SAR multiple moving target imaging method based on alternating direction method of multipliers (ADMM) is proposed by utilizing the multi-component linear frequency modulation signal form and sparse prior knowledge of synthetic aperture radar (SAR) multiple moving target signals, First, a sparse observation model of SAR multiple moving targets is established to formulate the multiple moving target imaging task into an inverse problem with the sparse feature constraint. Then the adaptive Chirplet decomposition method is applied to realize the estimation of target Doppler modulation frequencies for the observation matrix construction. The well-focused SAR image of multiple moving targets can be sparsely reconstructed based on ADMM decomposing the complex convex optimization problem into several simple subproblems which can be alternately solved. Finally, the simulations and the experiments on airborne SAR data show that the proposed method is superior to the existing moving target imaging methods in terms of imaging quality and imaging efficiency.