Compared with traditional gamma-ray imaging equipment, the Compton camera is a very promising imaging device in nuclear medicine and molecular imaging, and has a strong potential application in monitoring beams in heavy-ion-therapy because of its high efficiency feature. A demonstration device for heavy ion cancer treatment with complete intellectual property right has been built at Institute of Modern Physics, Chinese Academy of Sciences in Wuwei city of Gansu Province. At present the device is being up-graded, and the heavy ion cancer treatment is being generalized in national wide. In view of the broad prospects of heavy ion cancer treatment, the imaging resolution of Compton camera is analyzed theoretically, and three errors effecting the imaging resolution, which are energy resolution, position resolution of detector and the Doppler effect, are determined. Then the three errors are simulated by using the Geant 4 packages. The physical process in simulation is selected as the G4EMPenelopePhysics model, which makes the atomic shell cross section data for low energy physical process used directly. The Compton camera geometry consists of two layers of detectors. The layer close to $\gamma$ source is called detector and the other one is called absorption detector. The material of scatter detector is selected as low- Zsilicon and carbon, and the absorb detector is high- Zgermanium. The thickness value of scatter detector and absorb detector are both 20 mm. The spacing between the two layers is 100 mm. The simulation results by Geant 4 are used to reconstruct the image of point-like $\gamma$ source through using the back-projection algorithm. The simulation results and the re-constructed images indicate that the difference between the image full width at half maximum induced by 2 mm position resolution and that induced by 5.0% relative energy resolution of scatter detector is about 10%, and amount to that by the Doppler effect of Silicon. For the $\gamma$ ray with energies of several hundred keV, the energy resolution of Si detectors is easily better than 1.0% in practice. Therefore, the detector's position resolution dominates the image quality of the Compton camera. Considering the Doppler effect, manufacturing techniques and imaging efficiency, 2.0 mm-sized crystal unit and 1.0% energy resolution power is suggested for practically manufacturing the Compton camera.