In order to aim at a telescope system with large F number, long focal length, miniaturized dimension, high image quality and high stray light suppression, a three mirror off-axis anastigmatic telescope is designed based on the Cook type, of which f′ is 24 m, F number is 16, field of view is 1.6°×1°. The outer baffle and the structures inside are designed. The stray light of telescope system is analyzed with stray light program to calculate the point sources transmittance (PST). The forward and backward ray tracing is combined to find the key surface and modify the optical and mechanical structure with optimization and iteration. The result shows that the modulation transfer functions (MTF) approaches the diffraction limit at all fields. When the evadable angle out of the field is 40°, the PST is less than 10-11 and the system can achieve the requirement of stray light suppression.