Abstract: In order to solve the problem of low computational efficiency of maximum likelihood estimation (MLE) localization algorithm in synthetic aperture localization, an algorithm based on fractional Fourier transform (FrFT) is proposed. The implementation process of the proposed algorithm is as follows: First, the Fourier transform is performed in the fast-time domain, and range frequency focusing is achieved; Second, the azimuth signal is extracted at the peak of the range spectrum, then FrFT is applied to process the extracted signal, obtaining the localization image in the fractional domain; Third, a high-precision localization image is directly acquired through parameter-coordinate mapping. From the algorithmic perspective, on one hand, the computational complexity is reduced because FrFT can be implemented by means of the Fourier transform; On the other hand, the computational efficiency of the algorithm is further improved, as a two-step search strategy is adopted during the FrFT operation. Through simulations, a comparison is conducted between the FrFT localization algorithm and the MLE localization algorithm in synthetic aperture localization. The experimental results validate the high efficiency of the proposed algorithm.