Facilitated transport membranes is a promising strategy to fabricate efficient separation membranes for aromatic/aliphatic mixtures. However, building up selective channels with uniformly distributed facilitated transport sites is still challenging. In this study, Cu-TAPB-COF (CuCOF) nanosheets, a kind of metal-covalent organic frameworks (MCOFs), were synthetized and introduced into poly (ether-block amide) (Pebax®2533) matrix to construct facilitated transport membranes for toluene/n-heptane mixtures. As the aromatic skeleton linked by covalent interaction, CuCOF could provide continuous low mass transfer resistance channel. And Cu(I) exist in skeleton could serve as uniformly distributed facilitated transport sites and maintain a long-term stability. The resulting membrane exhibited a higher adsorption selectivity and lower swelling degree compared with pure Pebax membrane. The membrane exhibited high pervaporation separation performance for 50 wt% toluene/n-heptane mixture. When the filling contents of CuCOF was 2.0 wt%, the membrane achieved a permeation flux of 937 g m−2 h−1 and the separation factor of 4.7.