An ultraviolet imaging spectrometer was studied based on the principle of the small scale ultraviolet spectral instrument. The scheme composed of an off-axis parabolic mirror telescope and a single toroidal grating spectral imaging system was designed. The optimization of the optical system is the optimum processing for the parameters of the toroidal grating. The optical path function and the aberration equations of the grating were analyzed. The perfect anastigmatism conditions and imaging conditions of the single toroidal grating system were obtained. These two conditions that cannot be satisfied by the algebra calculation method limit the field of view and waveband of the spectrometer. The genetic algorithm was introduced to solve the problem. A solar-blind ultraviolet imaging spectrometer for 200-280 nm was designed to verify the design method. The optimum initial configuration was calculated and simulated. A system with F/# 5.7, focal length 102 mm and high spatial resolution was designed. The modulation transfer functions (MTF) of all fields of view are more than 0.65 in the waveband in the required Nyquist frequency (20 1p x mm(-1)). The design results indicate that the optical system theory can be applied to the small scale ultraviolet imaging spectrometer with high resolution and spectral broadband.