The obstacles in further improving the heat-transport performance of the graphene-based films root in the random stacking configuration of the graphene flakes and their agglomeration in solvents. In order to overcome these obstacles, we design one kind of quasi-bilayer graphene device composed of one upper narrow nanoribbon and one lower wide nanoribbon with absorbed perfluorophenylazide (PFPA) molecules. By investigating the thermal conductivity (TC) of the quasi-bilayer graphene without absorbed PFPA molecules, we find the TC will increase as the length and width increase, while the TC will decrease with the increase of the layer number. This indicates that a quasi-bilayer graphene flake of a large area and a small layer number will be beneficial to increasing its TC. Furthermore, in the presence of the PFPA molecules, the TC of the quasi-bilayer graphene, albeit suppressed by the PFPA molecules, is found to decrease slowly with the increase of the PFPA molecule number. This demonstrates a feasible way to fabricate the high-quality graphene-based films based on the technology of absorbing PFPA molecules. This research should be an important reference for designing the graphene-based thermal functional devices.