The low-lying spectra of 24,25,26 Ne and the structure of the pygmy dipole resonance (PDR) in 26 Ne have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus 25 Ne, which explains the observed unexpected decay of PDR to the excited states of 25 Ne. The large isoscalar component of PDR is also shown and the enhancement of the core excitation in neutron-rich Ne isotopes is conjectured.