Non-stoichiometric Nd[Mg0.5Sn0.5(1+x)]O3 (-0.04 ≤ x ≤ +0.04) - type samples were prepared using a traditional two-step solid-state sintering process. Their crystal structures, phase compositions, dielectric properties and lattice vibrational characteristics were identified in detail. Double perovskite Nd(Mg0.5Sn0.5)O3 with a monoclinic structure was distinguished as the main crystalline phase, pure phase was obtained when x < 0, and the sample [Nd(Mg0.5Sn0.49)O3] at x = -0.02 shows the excellent dielectric properties: εr = 18.74, Q × f = 47,979 GHz. Lattice vibrational characteristics were clarified with Raman and infrared active modes assigned and illuminated, accurately. The intrinsic properties were fitted by four-parameter semi-quantum model, which show that the low-frequency infrared modes yield a more significant contribution to permittivity and dielectric loss. Raman shifts of modes F2g(A) and F2g(B) correlate with dielectric constants negatively, which implies that the bond length has a positive correlation with permittivity. Full widths at half maximum of vibritional modes A1g(O) correlate with dielectric loss values positively and correlate with the degree of order (S) negatively.