Our calculations demonstrate that the intrinsic magnetism of boron nitride nanotubes ( BNNTs) can be induced by their open ends, and the resulting magnetic moment is sensitive to the chirality of BNNTs. It is found that BNNTs, a pure sp-electron system, present a tremendous spin-splitting larger than 1 eV and that B-rich-ended and N-rich-ended BNNTs exhibit "conjugate", spin-polarized, deep-gap states. Tremendous spin-splitting effects combined with considerable local spin-polarizations at the open ends make BNNTs significant for applications of nanoscale spintronics such as spin-polarized electron emitters.