The physicochemical properties of triglyme (G3) and tetraglyme (G4) solutions containing lithium bis(trifluoromethanesulfonyl)amide (LiTFSA) were investigated. The concentration of LiTFSA was altered from a dilute solution to an extremely concentrated one, forming the complexes [Li(glyme)1][TFSA]. The ionic conductivity of the LiTFSA/glyme solutions changed depending on the LiTFSA concentration and exhibited a maximum at ca. 1 mol·dm–3. The viscosities of the solutions monotonically increased with increasing concentration of LiTFSA. The self-diffusion coefficient of each species in the solutions, which was measured by the pulsed-field gradient spin–echo NMR (PGSE-NMR) method, decreased with increasing concentration. The diffusion coefficient of the glymes in relatively dilute LiTFSA solutions was higher than that of the Li+ cation and the [TFSA]− anion. As the concentration of LiTFSA increased, the difference between diffusion coefficients of the glyme and Li+ cation became less pronounced. The identical diffusion coefficient of the glyme and Li+ cation in the equimolar mixture of glyme–LiTFSA suggested the formation of a complex cation [Li(glyme)1]+ in the liquid. Unexpectedly, the ionicity Λimp/ΛNMR (dissociativity) of [Li(glyme)1][TFSA] was higher than that of excess glyme solutions of [Li(glyme)x][TFSA] (x > 1). This result is similar to that observed for mixtures of typical ionic liquids and cosolvents and is opposite to that observed for conventional organic electrolyte solutions. The evaporation of glyme from the quasi-ionic liquid [Li(glyme)1][TFSA] took place at ca. 200 °C, and the activation energy for the evaporation rate of the glymes from [Li(glyme)1][TFSA] was estimated to be ca. 63 kJ·mol–1, which appears to correspond to the activation energy for the desolvation of the glyme from [Li(glyme)1][TFSA]. The electrochemical impedance measurements revealed that the activation energy for the charge-transfer reaction of Li/Li+ at the liquid | Li metal interface was ca. 68 kJ·mol–1, which is in good agreement with that for desolvation of the glymes.