In the framework of the search for promising electrolytes for lithium-ion batteries, quantumchemical modeling of the structure, stability, and electronic properties of membranes based on LiNafion. nDMSO, n = 0–16) has been performed by the density functional theory method with inclusion of gradient correction and periodic conditions (PBE/PAW). Inasmuch as the key factor that determines the ionic conductivity is the degree of swelling of LiNafion in DMSO (according to calculations, for n = 8, the degree of swelling is close to 500%, and for n = 16, it is close to 700% by volume), similar membranes can be good candidates from the viewpoint of lithium ion transport (with barriers of 0.2–0.3 eV, which depend on n).