Tungsten/graphene composite was developed and demonstrated to have good mechanical and thermal properties. Density functional theory calculations were performed to investigate elastic constants, elastic anisotropies and isotropic elastic moduli, thermodynamic properties and minimum thermal conductivity of tungsten/graphene with and without a helium-vacancy pair, and tungsten/graphane and tungsten/ditungsten carbide (tungsten/W2C) composites. The results show that tungsten/graphene composite has more toughness when compared with pure tungsten metal. It is noticed that the minimum thermal conductivity of tungsten/graphene composite is higher, introducing a potential application in heat dissipation at high temperatures. We give an honest appraisal of the anisotropic and isotropic (polycrystalline) elastic properties of tungsten/graphene, tungsten/graphane, and tungsten/W2C carbide composites. In addition, the results show that the graphene layer is a strong trap for the He atom, while He affinity to the graphene layer is weaker to a single vacancy. The formation of the He-vacancy pair due to trapping effects near the W/graphene interface will help to reduce the concentration of impurities and defects in the tungsten matrix and maintain the inherent heat dissipation properties under irradiation.