In this paper, a solid acid catalyst (ZPS–PVPA–SO3H) was prepared by anchoring thiol group on zirconium poly(styrene-phenylvinyl-phosphonate)-phosphate (ZPS–PVPA), followed by oxidation of thiol groups to obtain sulfonic acid groups. The solid acid catalyst was characterized by XPS, X-ray, EDS, SEM, and TG-DSC. The successful preparation of sulfonic acid-functionalized ZPS–PVPA was confirmed. Subsequently, the catalytic performance of ZPS–PVPA–SO3H was investigated in the epoxidation of soybean oil. The results demonstrated that ZPS–PVPA–SO3H can effectively catalyze epoxidation of soybean oil with TBHP as an oxidant. Moreover, there was no significant decrease in catalytic activity after 5 repeated uses of the ZPS–PVPA–SO3H. Interestingly, the ZPS–PVPA–SO3H was kept in 2 mol/L of HCl overnight after the end of the seventh reaction, and the catalytic activity was gradually restored during the eighth to tenth cycles.