Abstract: The Shanghai Advanced Proton Therapy Facility (APTR) project, proposed by the Shanghai Institute of Applied Physics (SINAP) of Chinese Academy of Sciences, has finished in the commissioning stage. As the key component of APTR complex, the injector system is upgraded to accelerate proton beam to 7.0 MeV in the context of comprehensive localization and miniaturization. To pre-accelerate, longitudinally bunch and transversely focus the low-energy proton beam from ion source, a pre-injecting system Radio-Frequency Quadruple (RFQ) was designed. Based on fast bunching strategy, this RFQ, operated at 325 MHz, accelerates proton particles to 3.0 MeV. The phase advance has been taken into consideration, and parametric resonance has been carefully avoided by adjusting the vane parameters. The whole transmission efficiency has been optimized to 98.0% to meet the machining requirements and the emittance growth in horizontal and vertical directions are about 1.2%, 3.3% along the entire cavity. This paper mainly introduces the beam dynamics design schemes, main parameter selections, simulation results and tolerance analysis. It can provide important theoretical base for linear injection system of proton synchrotron-based therapy facility.