Abstract: The 81.25 MHz radio frequency quadrupole (RFQ) accelerator is the key equipment of low energy intense-highly-charged ion accelerator facility (LEAF). In order to ensure the RFQ can achieve a stable operation and high-quality beam supply, the RFQ cavity vacuum is required to reach an ultra-high vacuum of about 10⁻⁶ Pa. In this paper, the design of the vacuum system of LEAF RFQ is completed by the two-stage molecular pump scheme, and the process of vacuum system design and equipment selection are introduced in detail. In addition, VAKTRAK and MOLFLOW+ were used to simulate the vacuum distribution under the design scheme. At present, LEAF RFQ operates stably and efficiently, and the measured vacuum is about 1.4×10⁻⁶ Pa, which meets the requirements of beam supply and experiments. This work verifies the reliability of VAKTRAK and MOLFLOW+ results and accumulates experience for vacuum system design of high intensity heavy-ion accelerator facility (HIAF).