The adsorption and diffusion of H atoms on beta-PtO2(001) surface have been studied using first-principles calculations. The chemisorbed H atoms are found to bind preferentially on the top sites of O atoms due to the much larger adsorption energies with comparison to adsorption atop Pt atoms. The calculated energy barriers along the optimal diffusion paths are comparable with that of H diffusion on Pt(111). Within the WKB approximation, the nuclear quantum effects (NQEs) along the diffusion paths are investigated. It turns out that the NQEs are significant for the surface diffusion of H at room temperature and play a dominant role in cryogenic conditions.