Electronic properties of single-walled boron nitride nanotube in zig-zag form are numerically investigated by replacing B atoms with C atoms. Using a tight-binding Hamiltonian, the methods based on Green’s function theory, Landauer formalism and Dyson equation, the electronic density of states and electronic conductance in boron nitride nanotube and boron carbonitride nanotube are calculated. Our calculations indicate that in a boron nitride nanotube, the localized states associated with C impurities appear as the concentration of C atoms increases. The boron carbonitride nanotube thus behaves like a semiconductor. Also, by increasing the C atom concentration, the voltage in the first step on the $I–V$ characteristics decreases, whereas the corresponding current increases.