Solid polymer electrolytes are prepared by the combination of a polyether, poly(ethylene oxide) (PEO) or poly(ethylene oxide-co-propylene oxide) (P(EO/PO)), and a polyanionic lithium salt, (poly(lithium sorbate) (Poly(Li-Sorb)) or poly(lithium muconate) (Poly(Li-Muco)), and their ionic conductivities, lithium ion transference number, electrochemical stabilities, thermal properties, and mechanical strength were investigated in the absence and presence of BF3·OEt2. The ionic conductivities of all solid polymer electrolytes were enhanced by one to two orders of magnitude with addition of BF3·OEt2, because the dissociation of lithium ion and carboxylate anion was promoted by complexation with BF3. The lithium ion transference number in these solid polymer electrolytes showed relatively high values of 0.45–0.88, due to the suppression of the transport of the large counter polymeric anion. These solid polymer electrolytes showed good electrochemical and thermal stabilities, and also, the mechanical strength of the solid polymer electrolytes was improved by the function of crystalline poly(lithium carboxylate)s as a sort of filler.