The paper designs and improves a telecentric imaging spectrometer, the Dyson imaging spectrometer. The optical structure of the imaging spectrometer is simple and compact, which is only composed of a hemispherical lens and a concave grating. Based on the Rowland circle and refraction theory, the broadband anastigmatic imaging condition of Dyson imaging spectrometer which is the ratio of the grating radius and hemispherical lens radius has been analyzed. By imposing this condition for two different wavelengths, the parameters of the optical system presenting low aberrations and excellent imaging quality are obtained. To make the design spectrometer more suitable for the engineering application, the paper studies the method making the detector not to attach the surface of the hemispherical lens. A design example using optimal conditions was designed to prove our theory. The Dyson imaging spectrometer of which the imaging RMS radii are less than 2.5 μm and the advanced spectrometer of which the imaging RMS radii are less than 8 μm, with NA 0.33, waveband 0.38~1.7 μm and the slit length 15 mm, have been obtained. The design method and results are more feasible and predominant, and can be applied in the areas of the industry and remote sensing.