As spectroscopic detection technology rapidly advances, back-illuminated InGaAs detectors with a wider spectral range have emerged. Compared to traditional detectors such as HgCdTe, CCD, and CMOS, InGaAs detectors offer a working range of 400–1800 nm and exhibit a quantum efficiency of over 60% in both the visible and near-infrared bands. This is leading to the demand for innovative designs of imaging spectrometers with wider spectral ranges. However, the widening of the spectral range has led to the presence of significant axial chromatic aberration and secondary spectrum in imaging spectrometers. Additionally, there is difficulty in aligning the system optical axis perpendicular to the detector image plane, resulting in increased challenges during post-installation adjustment. Based on chromatic aberration correction theory, this paper presents the design of a wide spectral range transmission prism-grating imaging spectrometer with a working range of 400–1750 nm using Code V. The spectral range of this spectrometer covers both the visible and near-infrared regions, which is beyond the capability of traditional PG spectrometers. In the past, the working spectral range of transmission-type PG imaging spectrometers has been limited to 400–1000 nm. This study’s proposed chromatic aberration correction process involves selecting optical glass materials that match the design requirements and correcting the axial chromatic aberration and secondary spectrum, ensuring that the system axis is perpendicular to the detector plane and easy to adjust during installation. The results show that the spectrometer has a spectral resolution of 5 nm, a root-mean-square spot diagram less than 8 μm over the full field of view, and an optical transfer function MTF greater than 0.6 at a Nyquist frequency of 30 lp/mm. The system size is less than 90 mm. Spherical lenses are employed in the system design to reduce manufacturing costs and complexity while meeting the requirements of wide spectral range, miniaturization, and easy installation.