Graphene is a two-dimensional (2D) material with the thickness of one single atom. This material is a carbon allotrope with nanostructure lattice of hexagonally arranged carbon atoms [1]. Due to the particular shape of graphene, it has an extraordinary thermal conductivity which has been reported to be up to 3000 W/(m⋅K) [2, 3] and 5300 W/(m⋅K) [4] while thermal conductivities of polymers are usually less than 1W/(m⋅K). This huge difference between thermal conductivities of graphene and polymers, introduces graphene as a highly efficient filler to significantly enhance the thermal conductivity of polymers [4, 5]. In the calculation of thermal conductivity of such nanocomposite materials, agglomeration formation and polymer–graphene interfacial thermal resistance are two significant parameters which can restrict the improvement of thermal behavior [6, 7].However, the dispersion of nanofillers based on functionally graded (FG) patterns in the host matrix usually improves the overall thermal and mechanical performances of nanocomposite materials. Moreover, FG dispersions of nanofillers provide a better management on the thermomechanical responses of nanocomposite structures [8–13].