Inspired by the recently-reported strong electric-dipole (E1) transition between the weaklybound first and second excited states, 3/2 − at 765 keV and 1/2 + at 885 keV, in the nucleus 27 10 Ne 17 , the E1 transition is estimated in a model by properly taking into account the effect of both deformation and weakly-bound neutrons. In addition to both the spin-parities, 1/2 + and 3/2 − , and observed nearly degenerate energies of the two excited states, the observed order of magnitude of the E1 transition strength between the two states is very naturally explained in the case that these two excited states are prolately deformed, in terms of the transitions between the halo components of the wave functions of the weakly-bound odd-neutrons, s 1/2 → p 3/2 and s 1/2 → p 1/2 , in addition to the large probability of the p 3/2 component in the weakly-bound neutron [330 1/2] orbit. The large probability is the result of the shell-structure unique in weakly-bound or resonant neutrons. PACS numbers: