He-H synergistic effects influence the performance of structural materials in fusion reactors. Due to the lack of high-intensity fusion neutron sources, multiple ion beam irradiation has been widely used as an emulation method to study its synergistic effects. However, the damage rate under multiple ion beam irradiation is three to four orders of magnitude higher than that under fusion neutron irradiation, and its effect on the cavity swelling is still unclear. In this study, pure nickel was irradiated with single and triple ion beams to ~1 displacements per atom (dpa) at 450 °C. The damage rate ranged from 1.4 × 10−4 to 1.4 × 10−3 dpa/s, with the identical gas-dose ratios of ~400 H appm/dpa and 100 He appm/dpa. Large and isolated cavities formed under single ion irradiation, while triple ion irradiation induced smaller and denser cavities and higher swelling. As the damage rate increased, the cavity size, density, and swelling decreased, due to the constraint of cavity nucleation and growth processes. The effect of damage rate on cavity evolution under triple ion irradiation strongly depends on two competing factors: the enhancement of aggregation and binding of H/He/vacancies, and the enhancement of vacancies–interstitials recombination with increasing damage rate.