This research investigated the effect of functionalization on the thermal conductivity of multilayer graphene nanocomposites using molecular dynamics simulation. The functional groups grafted on the graphene surface are carboxyl and amine groups. The interfacial thermal conductance (ITC) between the graphene and the surrounding epoxy matrix was examined and the effects of the functional groups on ITC were explicated using vibrational density of state (VDOS). It was found that the VDOS mismatch between the surrounding epoxy and the outmost layer of graphene could be lessened by the functional groups. Nevertheless, the VDOS mismatch between the outmost layer and the inner layers within multilayer graphene was increased. Thus, the functional group grafted on the surface can effectively improve the ITC in the interface, but decrease the thermal conductivity of multilayer graphene. Moreover, the effect of layer number in the thermal conductivity of multilayer graphene was characterized through the Fourier’s law. Results indicated when the layer number increased, the thermal conductivity of multilayer graphene increased accordingly.