We investigate the electronic structures and electron emission properties of alkali-doped boron-nitride nanotubes (BNNTs) using density-functional theory calculations. We find that the nearly free-electron (NFE) state of the BNNT couples with the alkali atom states, giving rise to metallic states near the Fermi level. Unlike the cases of potassium-doped carbon nanotubes, not only the s but the d orbital state substantially takes part in the hybridization, and the resulting metallic states preserve the free-electron-like energy dispersion. Through first-principles electron dynamic simulations under applied fields, it is shown that the alkali-doped BNNT can generate an emission current 2 orders of magnitude larger than the carbon nanotube. The nodeless wave function at the Fermi level, together with the lowered work function, constitutes the major advantage of the alkali-doped BNNT in electron emission. We propose that the alkali-doped BNNT should be an excellent electron emitter in terms of the large emission current as well as its chemical and mechanical stability.