Using the van-der-Waals-corrected density functional theory (DFT) and molecular dynamic (MD) simulations, we theoretically predict the H2 separation performance of a new two-dimensional sp2 carbon allotropes-fused pentagon network. The DFT calculations demonstrate that the fused pentagon network with proper pore sizes presents a surmountable energy barrier (0.18 eV) for H2 molecule passing through. Furthermore, the fused pentagon network shows an exceptionally high selectivity for H2/gas (CO, CH4, CO2, N2, et al.) at 300 and 450 K. Besides, using MD simulations we demonstrate that the fused pentagon network exhibits a H2 permeance of 4 × 107 GPU at 450 K, which is much higher than the value (20 GPU) in the current industrial applications. With high selectivity and excellent permeability, the fused pentagon network should be an excellent candidate for H2 separation.