The heavy-ion accelerator RAON has the advantage of having both an in-flight (IF) and an isotope separator on-line (ISOL) system. Two radio frequency quadrupoles (RFQs) will be installed in the RAON: the main linear accelerator (LINAC) RFQ will be used to accelerate the two-charge state U-238 for the IF system, while the post-accelerator RFQ will be used to accelerate low-current isotope beams from the ISOL system. In this paper, the post-accelerator RFQ design for the ISOL system is reported. A beam current of 1 p mu A was used, and the input beam and the output beam energies were 5 keV/u and 400 keV/u, respectively. Moreover, the design was optimized by reducing the total length and power, adjusting the beam quality. To quantify the influence of thermal expansion on the frequency, we calculated the frequency difference according to deference between the vane's tip and the body's diameter.