Abstract: A 499.8 MHz SOLEIL-type superconducting cavity was simulated and designed for the first time in this paper. The higher-order mode (HOM) properties of the cavity were investigated. Two kinds of coaxial HOM couplers were designed. Using 4 L-type and 4 T-type HOM couplers, the longitudinal impedance and the transverse impedances were suppressed to below 3 kΩ and 30 kΩ/m, respectivly. The HOM damping requirements of Hefei Advanced Light Facility (HALF) were satisfied. This paper conducted an in-depth study on the radio frequency (RF) design, multipacting optimization, and thermal analysis of these coaxial couplers. Simulation results indicated that under operating acceleration voltage, the optimized couplers does not exhibit multiplicating or thermal breakdown phenomena. The cavity has the potential to reach a higher acceleration gradient.