The High-Resolution Imaging Camera (HiRIC) onboard China’s Tianwen-1 Mars probe aims to acquire detailed imagery of the Martian surface to comprehensively investigate its topography and geomorphology. The HiRIC is a pushbroom camera comprising three CCDs to simultaneously achieve sub-meter resolution and a large swath. However, processing HiRIC images using the conventional photogrammetric workflow is difficult due to the large shifts and narrow overlapping among the CCD lines. This paper presents a novel approach for photogrammetric processing of HiRIC images for precision topographic mapping that incorporates 1) the fitting of the initial Rational Polynomial Coefficients (RPCs) of images from the HiRIC position and pointing data, 2) a deep-learning-based method for tie-point matching between adjacent CCD images and cross-orbit images, 3) the bundle adjustment of multiple CCD images for tripled-epipolar image generation to ensure inner-orbit consistency, 4) the block adjustment of multiple orbit images to ensure cross-orbit consistency, and 5) dense image matching and space intersection based on the refined RPCs to generate Digital Elevation Models (DEMs). Experimental analyses were conducted using HiRIC images covering the landing region of the Zhurong rover. The results revealed that subpixel accuracy was achieved for image residuals among multiple-CCD or multiple-orbit images. Comparison with the reference data (HiRISE and MOLA DEMs) revealed a mean deviation of less than 7 m in terms of the geometric accuracy and the subtle topographic details of the HiRIC DEM. The presented approach offers a reliable solution for using the new dataset of HiRIC imagery for Mars topographic mapping.