Abstract: A compact synchrotron was designed based on beam optical software. The advantages of the synchrotron are small circumference, small aperture of magnet and high beam quality. The design of injection and extraction is very important for the synchrotron. Based on Matlab/AT, a simulation code of injection and extraction was developed, and the dynamic of injection and extraction process was studied. The result shows that the beam in the synchrotron has high quality, high injection rate and low beam loss in extraction process. The synchrotron can be used to study of spaceflight, material and biology.