  We have applied the Gamow shell model to calculate nuclear observables of
$^{26-31}$Ne isotopes pertaining to one-neutron halo structure, these nuclei
being situated close to neutron drip-line. As both many-body correlations and
continuum coupling are taken into account in that approach, halo structure can
be analyzed properly. Our calculations provide good descriptions of
$^{26-31}$Ne, where asymptotic behavior is crucial for that matter. One-body
density, neutron root-mean-square radii of $^{26-31}$Ne, and one-neutron
overlap functions of $^{29,31}$Ne have been calculated as well. Our results
support the presence of a one-neutron \textit{p}-wave halo in $^{31}$Ne,
already pointed out experimentally. A similar situation also occurs in the
ground state of $^{29}$Ne, which is mainly a \textit{p}-wave valence neutron
coupled to the inner $^{28}$Ne \textit{core}. The $3/2^+$ excited state of
$^{29}$Ne, which is dominated by a \textit{d}-wave valence neutron, has also
been considered. A larger radius and more extended wave function occur for the
ground state of $^{29}$Ne when compared to its $3/2^+$ first excited state. The
present results suggest that $^{29}$Ne is a good candidate for one-neutron
\textit{p}-wave halo in the medium-mass region.
