  Microscopic structure of the low-lying isovector dipole excitation mode in
neutron-rich $^{26,28,30}$Ne is investigated by performing deformed
quasiparticle-random-phase-approximation (QRPA) calculations. The particle-hole
residual interaction is derived from a Skyrme force through a Landau-Migdal
approximation. We have obtained the low-lying resonance in $^{26}$Ne at around
8.5 MeV. It is found that the isovector dipole strength at $E_{x}<10$ MeV
exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule. This
excitation mode is composed of several QRPA eigenmodes, one is generated by a
$\nu(2s^{-1}_{1/2} 2p_{3/2})$ transition dominantly, and the other mostly by a
$\nu(2s^{-1}_{1/2} 2p_{1/2})$ transition. The neutron excitations take place
outside of the nuclear surface reflecting the spatially extended structure of
the $2s_{1/2}$ wave function. In $^{30}$Ne, the deformation splitting of the
giant resonance is large, and the low-lying resonance is overlapping with the
giant resonance.
