Nonuniformly-rotating ship refocusing is very significant in the marine surveillance of satellite synthetic aperture radar (SAR). The majority of ship imaging algorithms is based on the inverse SAR (ISAR) technique. On the basis of the ISAR technique, several parameter estimation algorithms were proposed for nonuniformly rotating ships. But these algorithms still have problems on cross-terms and noise suppression. In this paper, a refocusing algorithm for nonuniformly rotating ships based on the bilinear extended fractional Fourier transform (BEFRFT) is proposed. The ship signal in a range bin can be modeled as a multicomponent cubic phase signal (CPS) after motion compensation. BEFRFT is a bilinear extension of fractional Fourier transform (FRFT), which can estimate the chirp rates and quadratic chirp rates of CPSs. Furthermore, BEFRFT has excellent performances on cross-terms and noise suppression. The results of simulated data and Gaofen-3 data verify the effectiveness of BEFRFT.