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For air-missile borne bistatic forward-looking beam-steering synthetic aperture radar (BFLBS-SAR), the receiver platform moves along a curve track due to the existence of accelerations. Besides, transmitting and receiving antenna beams rotate around a certain rotary center during the process of data collection to extend or shorten synthetic aperture time. These characteristics imply that the echo signal suffers serious range–azimuth coupling and aliasing problems of azimuth spectrum. Worse still, the echo process has problems of double-radical sign and high-order terms, which makes the rotary beam center unable to be obtained directly, and thus, the traditional polar formation algorithm (PFA) cannot be applied directly to BFLBS-SAR. To solve these problems, this paper proposes a generalized PFA (GPFA) for air-missile borne BFLBS-SAR. The algorithm uses the equivalent bistatic linear range model first to separate platform acceleration errors. By equating the bistatic mode to the monostatic one, an equivalent rotary center is obtained, and a new azimuth Deramp function is introduced to eliminate aliasing. Then, spectrum utilization and azimuth sampling rate are improved by spectral rotation and interpolation, and the image format is changed. In the azimuth focusing phase, azimuth aliasing is avoided by means of azimuth scaling, which makes azimuth focusing possible eventually. Numerous simulation experiments verify the effectiveness of the proposed GPFA.