In this paper, the squint mode multi-channel (MC) synthetic aperture radar (SAR) with hybrid baseline and fluctuant terrain is proposed and studied for high-resolution and wide-swath (HRWS) imaging. During the imaging process, due to the cross-track baseline and fluctuant terrain, the azimuth signal reconstruction is the kernel problem for this imaging mode. To deal with this problem, in this paper a robust azimuth signal reconstruction approach is proposed, where terrain elevation of scene is considered. At first, the pre-processing of the linear range cell migration correction (RCMC) and topography-independent phase compensation is implemented in the azimuth time domain. After that, combining the azimuth echo signal characteristics, the local polynomial Fourier transform (LPFT) is utilized to obtain the coarse-focused SAR image. Then, based on joint pixel pair vector and robust Capon beamforming (RCB), a Doppler ambiguity suppression approach is proposed to reconstruct the Doppler ambiguity-free azimuth signal in LPFT frequency domain, during which the influence of the cross-track baseline component and fluctuant terrain is eliminated using the coarse digital elevation model (DEM) for the imaging scene. At last, the chirp scaling imaging algorithm is utilized to focus the SAR image. The effectiveness of the proposed imaging approach is demonstrated via simulated and real measured squint mode MC-HRWS SAR data.