The quantum motions of hydrogen (H) atoms play an important role in the dynamical properties and functionalities of condensed phase materials as well as biological systems. In this work, based on the transfer matrix method and first-principles calculations, we study the dynamics of H atoms on Pt(111) surface and numerically calculate the quantum probability of H transferring across the surface potential fields. Atomic resonant tunneling (ART) is demonstrated along a number of diffusion pathways. Owing to resonant tunneling, anomalous rate of transfer is predicted for H diffusion along certain path at low temperatures.The role of nuclear quantum effects (NQEs) on the surface reactions involving H is investigated, by analyzing the probabilities of barrier-crossing. The effective barrier is significantly reduced due to quantum tunneling, and decreases monotonically with temperature within a certain region. For barrier-crossing processes where the Arrhenius type relation applies, we show the existence of a nonzero low-temperature limit of rate constant, which indicates the nontrivial activity of H-involved reactions at cryogenic conditions.