New glyme–Li salt complexes were prepared by mixing equimolar amounts of a novel cyclic imide lithium salt LiN(C2F4S2O4) (LiCTFSI) and a glyme (triglyme (G3) or tetraglyme (G4)). The glyme–Li salt complexes, [Li(G3)][CTFSI] and [Li(G4)][CTFSI], are solid and liquid, respectively, at room temperature. The thermal stability of [Li(G4)][CTFSI] is much higher than that of pure G4, and the vapor pressure of [Li(G4)][CTFSI] is negligible at temperatures lower than 100°C. Although the viscosity of [Li(G4)][CTFSI] is high (132.0mPas at 30°C), because of its high molar concentration (ca. 3moldm−3), its ionic conductivity at 30°C is relatively high, i.e., 0.8mScm−1, which is slightly lower than that of a conventional organic electrolyte solution (1moldm−3 LiTFSI dissolved in propylene carbonate). The self-diffusion coefficients of a Li+ cation, a CTFSI− anion, and a glyme molecule were measured by the pulsed gradient spin-echo NMR method (PGSE-NMR). The ionicity (dissociativity) of [Li(G4)][CTFSI] at 30°C is ca. 0.5, as estimated from the PGSE-NMR diffusivity measurements and the ionic conductivity measurements. Results of linear sweep voltammetry revealed that [Li(G4)][CTFSI] is electrochemically stable in an electrode potential range of 0–4.5V vs. Li/Li+. The reversible deposition-stripping behavior of lithium was observed by cyclic voltammetry. The [LiCoO2|[Li(G4)][CTFSI]|Li metal] cell showed a stable charge–discharge cycling behavior during 50 cycles, indicating that the [Li(G4)][CTFSI] complex is applicable to a 4V class lithium secondary battery.