Near space is the key to integrating “sky” and “space” into the future. A synthetic aperture radar (SAR) that works in this area would initiate a technological revolution for remote sensing applications. This study mainly focused on ground moving target imaging (GMTIm) for a near-space hypersonic vehicle-borne SAR (NS-HSV-SAR) with squint angle. The range history, parameter coupling, and Doppler ambiguity of the squint-looking NS-HSV-SAR are more complicated than traditional side-looking airborne or space-borne SARs. Thus, a precise range model is presented on the basis of phase error analyses. Then, all potential distributions of echo’s azimuth spectrum are derived, and a GMTIm method is proposed on the basis of a detailed analysis of the echo characteristics. The proposed method consists of three steps. Firstly, a prior information-based pre-processing function was created to decrease the Doppler ambiguity and range migration effects. Secondly, a blur matched keystone transform was developed to correct the residual range walk migration. Thirdly, a time-saving chirp Fourier transform was investigated for azimuth focusing. Implementation considerations, including the curvilinear trajectory of the NS-HSV-SAR, multiple moving target imaging, and applicability and limitation of the method, are discussed. Finally, simulation results are presented to validate the effectiveness of the proposed method.