Layer-by-layer-stacked chemical vapour deposition (CVD) graphene films find applications as transparent and conductive electrodes in solar cells, organic light-emitting diodes and touch panels. Common to lamellar-type systems with anisotropic electron delocalization, the plane-to-plane (vertical) conductivity in such systems is several orders lower than its in-plane conductivity. The poor electronic coupling between the planes is due to the presence of transfer process organic residues and trapped air pocket in wrinkles. Here we show the plane-to-plane tunnelling conductivity of stacked CVD graphene layers can be improved significantly by inserting 1-pyrenebutyric acid N-hydroxysuccinimide ester between the graphene layers. The six orders of magnitude increase in plane-to-plane conductivity is due to hole doping, orbital hybridization, planarization and the exclusion of polymer residues. Our results highlight the importance of interfacial modification for enhancing the performance of LBL-stacked CVD graphene films, which should be applicable to other types of stacked two-dimensional films.