A 350-MHz radio-frequency quadrupole (RFQ) accelerator in KOMAC is responsible for proton beam bunching, focusing, and acceleration up to 3 MeV. This RFQ was developed in 2003 and has been operated for about twenty years. Unfortunately, this RFQ suffered from low beam transmission and the deformation of the RFQ entrance, which is suspected of being damaged by arcing, was identified. Therefore, the new RFQ has been designed to replace the older one. The basic design parameters were determined by the PARMTEQ and the Poisson-Superfish code. A full 3-dimensional RFQ model was produced, and the electromagnetic field analysis was performed using the CST Studio Suite. The under-cut and the tuner were designed to satisfy the electromagnetic field distribution calculated by the Poisson-Superfish and the resonance frequency. In addition, we analyzed the mode frequency spectrum based on the 3D model of RFQ to design dipole-stabilizing rod.