Using density functional theory calculations, we have investigated the adsorption of Li+, Na+ and K+ cations on the surface of a BC2N nanotube in terms of energetic, geometric and electronic properties. The adsorption is site-selective, so that the cations prefer to be adsorbed atop a hexagonal ring of the tube surface which involves more N atoms. The adsorption energy of Li+ (-54.6 kcal/mol) is more negative than that of the others (about -41.5 kcal/mol for Na+ and -18.4 kcal/mol for K+). By increasing the number of adsorbed Li+ cation, the adsorption energy per a cation is decreased and also the HOMO, LUMO and Fermi level are more shifted to lower energies. The adsorption of the alkali cations may impede the electron emission from the BC2N nanotube surface by increasing the work function due to the charge transfer from the tube to the cation.