Understanding the transport and adsorption characteristics of hydrogen (H2) in calcium silicate hydrate (C-S-H) nanopores is critical to minimize the leakage risks from cement in the wellbore region during underground H2 storage (UHS). However, the critical physiochemical properties of H2 in C-S-H nanopores remain inadequately understood. In this work, we perform molecular dynamics simulations to comprehensively investigate the H2 distribution and diffusion properties in the C-S-H nanopores, considering the crucial parameters of temperature, pressure, and pore size. We evaluate how the density distribution, mean squared displacement (MSD) and diffusion coefficient of H2 evolve with variations in these crucial parameters by comparing H2 properties in C-S-H nanopores with those of bulk H2. We show that H2 molecules are prone to adsorb on C-S-H walls and form a high-density adsorption layer due to strong interactions between C-S-H walls and H2. We find that the confinement of C-S-H nanopores significantly limits the diffusion of H2, leading to smaller diffusion coefficients. Moreover, the diffusion of H2 demonstrates pronounced anisotropic characteristics, with H2 diffusing significantly faster in the direction parallel to C-S-H walls than in the direction perpendicular to the C-S-H walls. We demonstrate that there is a critical pressure, beyond which the diffusion coefficient of H2 parallel to C-S-H walls is close to that in the bulk phase and remains stable. We also show that the impact of nano-confinement gradually diminishes with increasing pore size. Under a given temperature/pressure condition, once the pore size exceeds a threshold, the H2 diffusion coefficient in the C-S-H nanopore is close to that of bulk H2. Our results provide valuable insights into H2 diffusion and adsorption in the C-S-H nanopores at the molecular level, which is critical to assessing and minimizing H2 leakage risks from cement in the wellbore.