A quasi-solid-state electrolyte consisting of tetraethylene glycol dimethyl ether (tetraglyme, G4)/lithium bis(trifluoromethanesulfonyl)amide (LiTFSA) mixtures together with fumed silica nanoparticles was prepared for use as the electrolyte of an all-solid-state lithium rechargeable battery. Via the liquid route, we have succeeded in fabricating a quasi-solid-state electrolyte regardless of the high concentration of G4/Li-TFSA such as 75 vol%. It was found that the conductivities, the self-diffusion coefficients and the structure of the G4/Li-TFSA complex in the quasi-solid-state composite are essentially similar to those of the bulks regardless of the solid-like appearance. Compared to the quasi-solid-state electrolytes containing the conventional room temperature ionic liquids (RTILs), the ones containing the equimolar G4/LiTFSA complex exhibited a higher stability to the lithium electrodes. The all-solid-state lithium rechargeable battery was assembled using LiCoO2 and lithium metal as the cathode active material and anode, respectively. The all-solid-state cells showed noticeable charge–discharge and cycle performances. In the cut-off voltage range of 4.3–3.4 V, it achieved high initial discharge capacities of 130, 110 and 90 mAh g−1 at 0.05, 0.1 and 0.2 C, respectively. Even after one hundred charge–discharge cycles, the discharge capacities remained high at 105, 100 and 95 mAh g−1, respectively.