Since the Doppler parameters vary according to the slant distance, the resolution is lower when using an imaging algorithm of traditional pulse compression in processing raw echo data of the missile-borne synthetic aperture radar (SAR). Moreover, an algorithm is proposed to solve these problems, which is based on the fractional Fourier transform (FrFT) for missile-borne SAR imaging. Firstly, an echo signal model is built for the terminal guidance stage of the missile-borne SAR. Secondly, the chirp rate of the echo signal is measured through the local optimum processing and obtains the optimum angles for the FrFT, and then the entire SAR image can be obtained by using FrFT with the optimum azimuth angles and operating range. Finally, the performances of the algorithms are assessed using simulated and real Radarsat-1 data sets. Results confirm that the FrFT-based missile-borne SAR processing methods can provide enhanced resolution that yields both lower-side lobes effects and improved target detection. The method introduced in this paper has important theoretical significance in detection and recognition of military targets and for precision guidance.