The Rare isotope Accelerator Of Newness (RAON) heavy-ion accelerator has been designed for the Rare Isotope Science Project (RISP) in Korea. The RAON will produce heavy-ion beams from 660-MeV-proton to 200-MeV/u-uranium with continuous wave (CW) power of 400 kW to support research in various scientific fields. Its system consists of an ECR ion source, LEBTs with 10 keV/u, CW RFQ accelerator with 81.25 MHz and 500 keV/u, a MEBT system, and a SC linac. In detail, the driver linac system consists of a Quarter Wave Resonator (QWR) section with 81.25 MHz and a Half Wave Resonator (HWR) section with 162.5 MHz, Linac-1, and a Spoke Cavity section with 325 MHz, Linac-2. These linacs have been designed to optimize the beam parameters to meet the required design goals. At the same time, a light-heavy ion accelerator with high-intensity beam, such as proton, deuteron, and helium beams, is required for experiments. In this paper, we present the design study of the high intensity RFQ for a deuteron beam with energies from 30 keV/u to 1.5 MeV/u and currents in the mA range. This system is composed of an Penning Ionization Gauge ion source, short LEBT with a RF deflector, and shared SC Linac. In order to increase acceleration efficiency in a short length with low cost, the 2nd harmonic of 162.5 MHz is applied as the operation frequency in the D + RFQ design. The D + RFQ is designed with 4.97 m, 1.52 bravery factor. Since it operates with 2nd harmonic frequency, the beam should be 50% of the duty factor while the cavity should be operated in CW mode, to protect the downstream linac system. We focus on avoiding emittance growth by the space-charge effect and optimizing the RFQ to achieve a high transmission and low emittance growth. Both the RFQ beam dynamics study and RFQ cavity design study for two and three dimensions will be discussed.