  The low-lying isovector dipole strengths in neutron rich nuclei $^{26}$Ne and
$^{28}$Ne are investigated in the quasiparticle relativistic random phase
approximation. Nuclear ground state properties are calculated in an extended
relativistic mean-field theory plus BCS method where the contribution of the
resonant continuum to pairing correlations is properly treated. Numerical
calculations are tested in the case of isovector dipole and isoscalar
quadrupole modes in the neutron rich nucleus $^{22}$O. It is found that in
present calculation low-lying isovector dipole strengths at $E_x < 10$ MeV in
nuclei $^{26}$Ne and $^{28}$Ne exhaust about 4.9% and 5.8% of the
Thomas-Reiche-Kuhn dipole sum rule, respectively. The centroid energy of the
low-lying dipole excitation is located at 8.3 MeV in $^{26}$Ne and 7.9 MeV in
$^{28}$Ne.
