A new linear injector called SSC-LINAC has been proposed to replace the Sector Focusing Cyclotron (SFC) for the Separator Section Cyclotron (SSC) and Cooling Storage Ring (CSR) of the Heavy Ion Research Facility of Lanzhou (HIRFL). Ions with ratio of mass to charge up to 7 are accelerated in the SSC-LINAC. The design research on a CW 53.667MHz RFQ accelerator will be presented. The beam dynamic design is based on 238 U 34+ beams with intensity of 0.5pmA. The inter-vane voltage is 70kV with the maximum modulation factor of 1.93. It uses a 2.5m long 4-rod structure to accelerate uranium ions from 3.728keV/u to 143keV/u with the transmission efficiency of 94%. The effect of different manufacturing crafts on beam dynamics has been checked. The specific shunt impedance has been optimized to 232.9kΩ·m. The water cooling system and design of the cavity tuning are also included in this paper.