The structural and electronic properties of β-SiC/(15, 0) carbon nanotube (CNT) and β-SiC/(16, 0)CNT core-shell structure are studied by using first-principles method based on the density functional theory. The results show that the two heterostructures are metallic. Their metallic properties are contributed by the atoms from the CNTs and the surface of SiC nanowires. The metallic property of the SiC nanowire is determined by its structure. However, the fact that the metallic (15, 0) and semiconducting (16, 0) CNTs both show the metallic properties after filling the SiC nanowires, is due to not the deformation of CNTs, but the charge transfer between CNTs and SiC nanowires.