Sparse microwave imaging is new concept, theory and methodology of microwave imaging, which introduces the sparse signal processing theory to microwave imaging and combines them together to overcome the paradox of increasing system complexity and imaging performance of current Synthetic Aperture Radar (SAR) systems. Traditional airborne SAR systems are facing a phase error problem in the echo which is caused by the non-ideal motion of the aircraft. This phase error could be compensated by autofocus algorithms. But in the sparse microwave imaging, such autofocus algorithm are no longer valid because traditional signal processing based on matched filtering has been replaced with sparse reconstruction. Current autofocus algorithms under sparse constraints are usually based on a two-step iteration, which convergences slowly and costs plenty of computation. In this paper, we introduce the Map-Drift (MD) autofocus algorithm to the accelerated sparse microwave imaging algorithm based on SAR raw data simulator, and propose the novel “MD-SAR raw data simulator autofocus algorithm”. This algorithm keeps the advantages of both accelerated imaging algorithm and MD algorithm, including the fast convergence and accurate compensation of two-order phase error in echo. Compared with current algorithms based on two-step iteration, the propose method convergences fast and effectively.