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The imaging of high-speed high-squint synthetic aperture radar (HSHS-SAR), which is mounted on maneuvering platforms with curved trajectory, is a challenging task due to the existence of 3-D acceleration and the azimuth spatial variability of range migration and Doppler parameters. Although existing imaging algorithms based on linear range walk correction (LRWC) and nonlinear chirp scaling (NCS) can reduce the range–azimuth coupling of the frequency spectrum (FS) and the spatial variability of the Doppler parameter to some extent, they become invalid as the squint angle, speed, and resolution increase. Additionally, most of them ignore the effect of acceleration phase calibration (APC) on NCS, which should not be neglected as resolution increases. For these issues, a modified frequency nonlinear chirp scaling (MFNCS) algorithm is proposed in this paper. The proposed MFNCS algorithm mainly includes the following aspects. First, a more accurate approximation of range model (MAARM) is established to improve the accuracy of the instantaneous slant range history. Second, a preprocessing of the proposed algorithm based on the first range compression, LRWC, and a spatial-invariant APC (SIVAPC) is implemented to eliminate most of the effects of high-squint angle and 3-D acceleration on the FS. Third, a spatial-variant APC (SVAPC) is performed to remove azimuth spatial variability introduced by 3-D acceleration, and the range focusing is accomplished by the bulk range cell migration correction (BRCMC) and extended secondary range compression (ESRC). Fourth, the azimuth-dependent characteristics evaluation based on LRWC, SIVAPC, and SVAPC is completed to derive the MFNCS algorithm with fifth-order chirp scaling function for azimuth compression. Consequently, the final image is focused on the range time and azimuth frequency domain. The experimental simulation results verify the effectiveness of the proposed algorithm. With a curved trajectory, HSHS-SAR imaging is carried out at a 50° geometric squint angle and 500 m × 500 m imaging width. The integrated sidelobe ratio and peak sidelobe ratio of the point targets at the scenario edges approach the theoretical values, and the range-azimuth resolution is 1.5 m × 3.0 m. [ABSTRACT FROM AUTHOR]