It is well known that ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler phase broadening, and velocity ambiguity caused by target unknown motion parameters, especially for the accelerating targets within a long observation time. To deal with these problems, a maneuvering target refocusing method based on keystone transform (KT) and coherently integrated cubic phase function (CICPF) is proposed in this paper. First, an azimuth deramp function is constructed along the slow-time dimension at each range-frequency gate to reduce the order of envelope migration and phase response over the slow-time. Then, the residual range walk and the time-varying Doppler phase are eliminated by the KT and the CICPF, respectively. With the estimated motion parameters, moving targets can be finely refocused. Both simulated and real SAR data processing results are presented to validate the proposed algorithm.