On the basis of density functional theory, we systematically investigate the electronic and magnetic properties of hybrid BN-C nanotubes, C x(BN)y where x + y = 12, with and without an external electric field. The BN-C nanotubes are totally distinct from pristine boron-nitride and carbon nanotubes. The electronic properties of C x(BN)y change significantly with composition: from the nonmagnetic semiconductors to the half-metals. The half-metallicity is attributed to the competition among the band gap, which is related to the width of C domain, the width of BN domain, and the intrinsic polarization field. Application of the external fields can enhance or counterbalance the polarization fields and change the band gaps. The half-metallicity can be modulated. In BN-rich tubes, such as C2(BN)10, the energy gap can be engineered from 0.50 eV to 0.95 eV and in C3(BN) 9, the ground state is converted from the nonmagnetic state into the anti-ferro-magnetic one. In other tubes, the half-metallicity can be enhanced or destroyed by different external fields. The modulation indicates that hybrid BN-C nanotubes can work as the components of the spin-filter devices.