A vortex synthetic aperture radar (SAR) can obtain more target information when combined with orbital angular momentum (OAM). However, ground-moving targets can cause image defocusing owing to their azimuthal velocity component and imaging position offset issues due to their range velocity component. However, more information on moving targets can be acquired for analysis using vortex SAR. This study first established an imaging model to extract moving target information from vortex echo signals. The target Doppler parameters were then estimated, and an improved range-Doppler algorithm was applied to compensate for the Bessel term and azimuthal phase term. A new azimuth-matched filter was designed based on the Doppler parameters to achieve focused imaging of moving targets. The simulation results verified the effectiveness of the proposed algorithm, and its performance was compared with that of plane-wave SAR. Vortex SAR offered better target quality parameters and azimuth resolution for the same synthetic aperture length. The proposed algorithm can effectively improve the azimuthal imaging of moving targets in low-tomoderate OAM modes.