The compound diffractive telescope is a novel space optical system which combines the structure of compound eyes with diffractive optics and so it has a lighter weight, a wider field of view （FOV）, a lower cost as well as looser fabrication tolerance. In this paper, the design of a compound diffractive telescope composed of one primary lens and twenty-one eyepieces is introduced. Then the influence of diffraction orders on the performance of the system is analysed. A modified phase function model of diffractive optics is proposed to analyse the modulation transfer function （MTF） curves for 0° FOV, which provides a more accurate prediction of the performance of the system. In addition, an optimized mechanism is also proposed to suppress stray light. The star image and resolution tests show that the system can achieve diffraction limit imaging within ±2° of FOV and 4-4 mm of eccentricity. Finally, a series of pictures of an object are taken from different channels, and the splicing of pictures from adjacent FOVs is demonstrated. In summary, the designed system has been proved to have great potential applications.
