By using non-equilibrium Green's function method, we investigate the thermoelectric properties of the molecular junctions based on acene-linked graphene nanoribbons. In this paper, effects of the length of the acene molecule, the contact position between the acene molecule and graphene nanoribbon electrodes on the thermoelectric parameters is mainly considered. It is found that the phonon contribution is dominant in the thermal conductance corresponding to the maximum of the thermoelectric figure of merit (<i>ZT<sub>max</sub></i>). As the length of the acene molecules increases, the phonon thermal conductance decreases monotonically, and eventually becomes almost independent of the acene molecules’ length. When the acene molecules are in contact with the middle (upper) part of the left (right) electrode of graphene nanoribbons, the corresponding <i>ZT<sub>max</sub></i> is highest. However, when the acene molecules are in contact with the middle (middle) part of the left (right) electrode of graphene nanoribbons, the corresponding <i>ZT<sub>max</sub></i> is lowest. When the temperature increases, <i>ZT<sub>max</sub></i> has an monotonously increasing tendency, regardless of the contact position. With the increase of the length of the acene molecules, the chemical potential corresponding to <i>ZT<sub>max</sub></i> 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.