Snapshot hyperspectral imaging is superior to scanning spectrometers due to its advantage in dimensionality, allowing longer pixel dwell time and higher data cube acquisition efficiency. Due to the trade-off between spatial and spectral resolution in snapshot spectral imaging technologies, further improvements in the performance of snapshot imaging spectrometers are limited. Therefore, we propose a cemented-curved-prism-based integral field spectrometer (CIFS), which achieves high spatial and high spectral resolution imaging with a high numerical aperture. It consists of a hemispherical lens, a cemented-curved-prism and a concave spherical mirror. The design idea of aplanatic imaging and sharing-optical-path lays the foundation for CIFS to exhibit high-resolution imaging in a compact structure. The numerical model between the parameters of optical elements and the spectral resolution of the system is established, and we analyze the system resolution influenced by the hemispherical lens and the cemented-curved-prism. Thus, the refractive index requirements of the hemispherical lens and the cemented-curved-prism for the optimal spatial and spectral resolution imaging of the system are obtained, providing guidance for the construction of CIFS. The designed CIFS achieves pupil matching with a 1.8 f-number lenslet array, sampling 268 × 76 spatial points with 403 spectral channels in the wavelength band of 400 to 760 nm. The spectral and spatial resolution are further evaluated through a simulation experiment of spectral imaging based on Zemax. It paves the way for developing integral field spectrometers exhibiting high spatial and high spectral resolution imaging with high numerical aperture.