Due to the significant azimuth variance property in medium-Earth-orbit (MEO) synthetic aperture radar (SAR) echo, it is difficult for the conventional SAR algorithms to achieve a good compromise between accuracy and efficiency. A novel algorithm based on Keystone transform (KT) and azimuth perturbation (AP) is introduced in this paper to handle this problem. The function of KT is to correct the range walk and thus to mitigate the azimuth variance effect on range processing. The function of AP is to equalize the Doppler histories in each range gate and thus to mitigate the azimuth variance effect on azimuth compressing. Simulation results of an L-band MEO SAR with 5 m resolution at 10,000 km altitude demonstrate the capability of our algorithm.