Solid electrolytes are a potential candidate for mitigating the safety issues associated with organic liquid-electrolyte-based conventional Lithium-Ion Batteries (LIBs). The film-forming ability, cost-effective fabrication, and superior interfacial contact of solid polymer electrolytes make them particularly appealing for application in all-solid-state LIBs (ASSLIBs). However, their practical applications are limited owing to their low lithium-ion conductivity and inadequate mechanical strength. In this study, we fabricated a highly flexible, soft, self-standing, and stable composite solid polymer electrolyte (CSPE) using poly(propylene carbonate) (PPC) as the main matrix and Na-superionic-conductor-type Li1.5Al0.5Ge1.5(PO4)3 (LAGP) as the active inorganic filler. The fabricated CSPE exhibited an attractive ionic conductivity of ∼0.56 mS∙cm−1, a wide electrochemical potential stability of ∼5 V vs. Li/Li+, a high lithium-ion transference number of ∼0.77, outstanding stability up to 1000 cycles of lithium plating/stripping, and better compatibility with lithium metal. In addition to these outstanding properties, the Li/CSPE/LiFePO4 (Li/CSPE/LFP) cell exhibited an impressive discharge capacity of 151 mAh∙g−1 at 0.1 C. Furthermore, at a rate of 1 C, the Li/CSPE/LFP cell delivered an initial discharge capacity of 96 mAh∙g−1, with a capacity retention of 63% over 1000 cycles. The interaction of lithium ions with the PPC was confirmed based on solid-state MAS NMR and XPS. The enhanced electrochemical performance of the CSPE is ascribed to the interaction of the LAGP filler with the PPC matrix, which forms a good polymer-inorganic interface, enabling the rapid lithium-ion transport. The proposed LAGP-reinforced CSPE presents new opportunities for the fabrication and engineering of ASSLIBs.