  It is known that nuclear deformation plays an important role in inducing the
halo structure in neutron-rich nuclei by mixing several angular momentum
components. While previous theoretical studies on this problem in the
literature assume axially symmetric deformation, we here consider non-axially
symmetric deformations. With triaxial deformation, the $\Omega$ quantum number
is admixed in a single-particle wave function, where $\Omega$ is the projection
of the single-particle angular momentum on the symmetric axis, and the halo
structure may arise even when it is absent with the axially symmetric
deformation. In this way, the area of halo nuclei may be extended when triaxial
deformation is considered. We demonstrate this idea using a deformed
Woods-Saxon potential for nuclei with neutron number N=13 and 43.
