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This article would like to provide an optimal beam steering control method for high-speed maneuvering platform synthetic aperture radar (SAR) imaging. A corresponding imaging algorithm with 3-D spatial-variation correction is proposed. First, the coordinates of beam footprint are calculated by the transition rule in each pulse repetition time (PRT). The transition rule is designed to get a unified image resolution and minimize the Doppler bandwidth. By the proposed imaging algorithm, 2-D spatial-variation envelop is corrected by azimuth keystone transform and range chirp scaling. Then the space-variant (SV) Doppler terms are compensated by frequency domain perturbation and time-domain resampling. The SV components in both the second- and third-order terms are removed. Finally, the proposed beam steering method and the imaging algorithm are verified by simulated SAR data.