By using non-equilibrium Green’s function method, we investigate the thermoelectric properties of molecular junctions based on acene-linked graphene nanoribbons. The effects of the length of the acene molecule, the contact position between the acene molecule and graphene nanoribbon electrode on the thermoelectric parameters are mainly considered in this work. It is found that the phonon contribution is dominant in the thermal conductance corresponding to the maximum of the thermoelectric figure of merit (ZT_max). As the length of the acene molecule increases, the phonon thermal conductance decreases monotonically, and eventually becomes almost independent of the acene molecule’ length. When the acene molecules contact the middle (upper) part of the left (right) electrode of graphene nanoribbon, the corresponding ZT_max is the highest. However, when the acene molecules contact the middle (middle) part of the left (right) electrode of graphene nanoribbons, the corresponding ZT_max is the lowest. As the temperature increases, ZT_max has a monotonically increasing tendency, regardless of the contact position. With the increase of the length of the acene molecule, the chemical potential corresponding to ZT_max becomes closer to the intrinsic Fermi level. The above findings may provide the valuable reference for the future design of thermoelectric devices based on the acene molecular junctions.