A compositionally homogeneous nonlinear optical single crystal of double-doped LiNbO3:Gd3+(0.003):Mg2+(0.65 wt.%) was obtained. Fine features of the LiNbO3:Gd3+(0.003):Mg2+(0.65 wt.%) crystal structure were studied from the Raman spectra of the first and second orders upon excitation by laser lines in the visible (532 nm) and near-IR (785 nm) regions. When the Raman spectrum was excited by a 785 nm laser line in the frequency range of 1000–2000 cm−1 for the first time, a number of low-intensity lines in the range of 900–2000 cm−1, corresponding to the second-order Raman spectrum, were discovered. The same lines also appear in the spectrum upon excitation by a laser line with a wavelength of 532 nm, but their intensities are significantly (by an order of magnitude or more) lower. It is shown that in the structure of the double-doped LiNbO3:Gd3+(0.003):Mg2+(0.65 wt.%), the crystal oxygen-octahedral clusters MeO6 (Me–Li, Nb, Gd, Mg) are slightly distorted, and in addition, the value R = [Li]/[Nb] ≈ 1 is close to that for a nominally pure stoichiometric crystal.