Using the China Spallation Neutron Source (CSNS) linac as the injector, a 500MeV proton synchrotron is proposed for multidisciplinary application, such as biology, material and proton therapy. The synchrotron will deliver proton beam with energy from 80 MeV to 500 MeV. A compact lattice design was worked out, and all the important beam dynamics issues were investigated. The 80 MeV H -beam is stripped and injected into the synchrotron by using multi-turn injection. In order to continuously extraction the proton with small beam loss, the achromatic structure is proposed and slow extraction method with RF knock-out is adopted and optimized.