Abstract: A compact cyclotron as the injector of a synchrotron which forms the heavy ion medical machine is being designed and constructed at Institute of Modern Physics, China. The required high intensity and high beam quality of the extraction beam make it difficult to design the extraction system. The magnetic field used in the design is calculated from TOSCA model. The single particle orbit is calculated to determine component types and basic parameters of the extraction system. The multi-particle tracking is done to determine the final component parameters and beam parameters. In order to improve the efficiency and beam quality of the extraction system, a C-type magnet is placed at the location, where the magnetic field gradient is very large. A pair of coil is used to eliminate the effect of the C-type magnet on the main magnetic field. Detailed calculations show the extraction beam intensity and beam quality can meet the requirement of the synchrotron.