Electronic structure and optical properties of a (5, 5) single-walled silicon carbide nanotube are studied with first principles calculation based on density functional theory. Depression and salient are formed near CSi defect and SiC defect in the surface of the nanotube. Defect energy levels are formed near the bottom of conduction band, which results in an n-type conductivity for nanotubes with antisite defects. In dielectric functions parallel and perpendicular to the axis of the nanotube, novel resonance peak is formed from transitions between top of the conduction band and the defect energy level.