Structures and properties of single walled (n,n) BN nanotubes doped with the C atom at different positions are studied by the DFT B3LYP/3-21G(d) theoretical method combined with the one-dimensional (1D) periodic boundary conditions. Their structure parameters, energies, stabilities, band structures and the energy gaps are explored. For the BN nanotubes doped with the C atom at different positions, the C atom concentrations x=1/4n (n=3–9) are examined. It is found that the N site tubes are almost undistorted and more stable. The band gaps are within 1.054–2.411 eV for the C atom doped at the B sites, and those are narrower and within 0.252–1.207 eV for the N sites. All of the doped tubes are shown to be semiconducting and have direct gaps.