Using the first-principles method, the electronic properties of the armchair and the zigzag C/SiC nanotube heterojunctions are investigated. Both heterjunctions exhibit semiconducting behaviors with a direct energy band. For the armchair heterojunction, type I heterojection is formed at the interface between the C and the SiC nanotubes, and the electrons and holes are confined in the C nanotube part. In the zigzag heterojunction, the electrons are localized in the C nanotube part, whereas the holes are distributd in the heterojunction uniformly. These heterojunctions can be good candidates for the future nano-devices.