Two-dimensional nanopores are very promising for high-permeance molecular sieving, but the molecular backflow from permeate-side to feed-side is not beneficial for improving molecular permeance. We study the quasi-unidirectional molecular transport through a graphene-hexagonal boron nitride bilayer nanopore, aiming to realize a high-permeance molecular sieving. Molecular dynamics simulations of CO2/CH4 separations show that the bilayer pore presents 3.7 times higher selectivity comparing to the single-layer graphene nanopore with the same size. The quasi-unidirectional molecular transport is attributed to the distinctive adsorption abilities of gas molecules on the two sides of bilayer nanopores and the inhibited molecular backflow from permeate-side to feed-side. This work provides a promising way to realize the ultra-permeable porous membranes with molecular permeance even higher than the single-layer atomic-thickness membranes.