Solid-state polymer electrolytes (SPEs) with high ionic conductivity are desirable for next generation lithium- and sodium-ion batteries with enhanced safety and energy density. Nanoscale fillers such as alumina, silica, and titania nanoparticles are known to improve the ionic conduction of SPEs and the conductivity enhancement is more favorable for nanofillers with a smaller size. However, aggregation of nanoscale fillers in SPEs limits particle size reduction and, in turn, hinders ionic conductivity improvement. Here, a novel poly(ethylene oxide) (PEO)-based nanocomposite polymer electrolyte (NPE) is exploited with carbon quantum dots (CQDs) that are enriched with oxygen-containing functional groups. Well-dispersed, 2.0-3.0 nm diameter CQDs offer numerous Lewis acid sites that effectively increase the dissociation degree of lithium and sodium salts, adsorption of anions, and the amorphicity of the PEO matrix. Thus, the PEO/CQDs-Li electrolyte exhibits an exceptionally high ionic conductivity of 1.39 × 10-4 S cm-1 and a high lithium transference number of 0.48. In addition, the PEO/CQDs-Na electrolyte has ionic conductivity and sodium ion transference number values of 7.17 × 10-5 S cm-1 and 0.42, respectively. It is further showed that all solid-state lithium/sodium rechargeable batteries assembled with PEO/CQDs NPEs display excellent rate performance and cycling stability.