Solid polymer electrolytes based on a novel comb-like copolymer, polyethylene glycol-grafted sulfonated polyether ether ketone (SPEEK-g-PEG), was designed and synthesized through the reaction between partially hydroxyl-functionalized sulfonated polyether ether ketone (SPEEK) and epoxy-functionalized PEG. The resulting SPEEK-g-PEG was fully characterized by FTIR, 1H NMR, TGA, and DSC. All data proved the successful grafting of PEG onto the SPEEK main chain. The resulting comb-like structure effectively inhibited the crystallization of PEG. After doping with a lithium salt, the obtained SPEEK-g-PEG polymer electrolyte membrane showed an improved ionic conductivity. The effects of chain length and PEG grafting ratio on the ionic conductivity of SPEEK-g-PEG were also investigated by electrochemical impedance spectroscopy (EIS). Moreover, the effect of this comb-like structure on increasing the ionic conductivity is higher than that of SPEEK/PEG blends, making these comb-like SPEEK-g-PEG copolymers attractive for an application in LIBs.