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A new linac injector CSR-LINAC for the Cooler Storage Ring of the Heavy Ion Research Facility in Lanzhou (HIRFL-CSR) is proposed to improve the per-formance of the HIRFL.As a key component of the CSR-LINAC, the 108.48-MHz radio frequency quadrupole (RFQ) is under design at the Institute of Mode Physics. Heavy ions with mass-to-charge ratios of 3-7 will be accelerated from 4 to 300 keV/u by the RFQ.In the beam dynamics design, the New Four-Section Procedure is adopted to improve the transmission efficiency and obtain a compact structure. In this paper, a transmission efficiency of 98.0% in the 3.07-m-long cavity was obtained. The Interdigital H-type structure is employed because of its mechanical stability and high shunt impedance. The RF performance of the cavity is investigated by the electro-magnetic simulation. The optimized results of the electric field to meet the beam dynamics requirements are pre-sented in this paper.