This letter proposes an algorithm for airborne synthetic aperture radar (SAR) ground moving target imaging (GMTIm) and motion parameters estimation (MPE), which is applicable in situations whether the Doppler ambiguity occurs or not. To derive the algorithm, the general expression for the received signal after range compression is deduced first, in which the useless exponential term induced by the possible Doppler ambiguity is omitted. Then, the second-order keystone transform (SOKT) is used to correct the range curvature. After the SOKT, the Radon transform is employed to estimate the slope of the target trajectory, and the range walk correction follows. In the following, the scaled Fourier transform and the dechirp technique are utilized to estimate the azimuthal parameters. Finally, the target's motion parameters are obtained by solving equations according to the trajectory slope and the estimated azimuthal parameters, with which the target is focused through azimuth matched filtering. Both simulated and real airborne SAR data are processed to validate the effectiveness of the proposed algorithm.