A supercell of a nanotube heterojunction formed by an (8, 0) carbon nanotube (CNT) and an (8, 0) silicon carbide nanotube (SiCNT) is established, in which 96 C atoms and 32 Si atoms are included. The geometry optimization and the electronic property of the heterojunction are implemented through the first-principles calculation based on the density functional theory (DFT). The results indicate that the structural rearrangement takes place mainly on the interface and the energy gap of the heterojunetion is 0.31 eV, which is narrower than those of the isolated CNT and the isolated SiCNT. By using the average bond energy method, the valence band offset and the conduction band offset axe obtained as 0.71 and -0.03eV, respectively.