We report the thermal conductance induced by few-layered graphene (G) sandwiched between β-phase tungsten (β-W) films of 15, 30 and 40 nm thickness. Our differential characterization is able to distinguish the thermal conductance of β-W film and β-W/G interface. The cross-plane thermal conductivity (k) of β-W films is determined at 1.69~2.41 Wm-1K-1 which is much smaller than that of α-phase tungsten (174 Wm-1K-1). This small value is consistent with the large electrical resistivity reported for β-W in literatures and in this work. The β-W/β-W and β-W/G interface thermal conductance (G W/W and G W/G ) are characterized and compared using multilayered β-W films with and without sandwiched graphene layers. The average G W/W is found to be at 280 MW m-2K-1. G W/G features strong variation from sample to sample, and has a lower-limit of 84 MW m-2K-1, taking into consideration of the uncertainties. This is attributed to possible graphene structure damage and variation during graphene transfer and W sputtering. The difference between G 2W/G and G W/W uncovers the finite thermal resistance induced by the graphene layer. Compared with up-to-date reported graphene interface thermal conductance, the β-W/G interface is at the high end in terms of local energy coupling.