According to the application requirements for remote sensing of upper atmosphere, a reflective optical system of spaceborne far ultraviolet hyperspectral imager is designed. Which is composed of a scan mirror, an off-axis parabolic telescope and a toroidal grating spectrometer. An aberration-correction method for concave toroidal grating is developed. The initial parameters are solved based on the geometrical aberration theory of concave grating and then optimized using the optical design software Zemax, and the toroidal gating spectrometer is designed. The root mean square of spot radius is less than 16 μm in the working waveband. Aberration is corrected simultaneously in broadband and the requirement of spectral resolution of 0.6 nm is satisfied, which indicates the aberration-correction method is feasible. Ray tracing and analysing are performed by Zemax software. Analyzed results demonstrate that the modulation transfer function for different wavelength is more than 0.8, which satisfies the design requirements. The construction is compact and suitable for application in space remote sensing.