Polar group-modified crosslinked polyethylene (XLPE) materials are developed with a peroxide thermochemical method of individually grafting chloroacetic acid allyl ester (CAAE) and maleic anhydride (MAH) to polyethylene molecular-chains, which are dedicated to ameliorating dielectric characteristics through charge-trapping mechanism. By free radical addition reactions, the CAAE and MAH molecules are successfully grafted to polyethylene molecular chains of XLPE in crosslinking process, as verified by infrared spectroscopy molecular characterizations. Dielectric spectra, electric conductance, and dielectric breakdown strength are tested to evaluate the improved dielectric performances. Charge trap characteristics are investigated by analyzing thermal stimulation depolarization currents in combination with first-principles electronic-structure calculations to reveal the polar-group introduced mechanisms of contributing dipole dielectric polarization, impeding electric conduction, and promoting electrical breakdown field. The grafted polar-group molecules, especially for MAH, can introduce deep-level charge traps in XLPE materials to effectively restrict charge injections and hinder charge carrier transports, which accounts for the significant improvements in electric resistance and dielectric breakdown strength.