Recently, a new phase C1’ H2 hydrate was experimentally identified. In this work, the diffusive behaviors of H2 in C1’ phase clathrate hydrate are explored using classic molecular dynamics (MD) simulations. It is revealed that the cage occupancy by H2 molecule negligibly influences the C1’ phase clathrate structure but greatly dictates the diffusion coefficient of H2 molecule. Due to the small cage size and small windows connecting the neighboring cages in C1’ phase clathrate, non-occupancy of the neighboring cages is demanded to enable the diffusion of H2 molecule that is primarily dominated by hopping mechanism. Moreover, the analysis of diffusive free energy landscape reveals lower energy barrier of H2 molecule in C1’ phase clathrate hydrate than that of other gases in conventional clathrate hydrates, and that H2 molecule travels through the windows between neighboring cages with preferential molecular orientation. This study provides critical physical insights into the diffusion behaviors of H2 in the C1’ phase clathrate hydrate, and implies that the C1’ clathrate hydrate is a promising solid structure for next-generation H2 storage.