The characteristics and principle of prism spectrometer are studied and a new method to design the prism spectrometer system with a small incident angle is proposed. This type of spectrometer uses reflective triplet optical path, so there is no need to add the correcting lens. The system has no aberration caused by the chromatic abberation and has excellent imaging quality. The spectral inflection can be corrected effectively. An optical system of imaging spectrometer is designed. The imaging quality is analyzed by using optical design software. The result shows that the modulation transfer function (MTF) of the system at different wavelengths is close to the diffraction limit and the design requirements are fully met.