The preparation of commodity polymers that can undergo self-healing of scratched surfaces is still quite challenging without involving complicated synthetic processes and high cost of healing agents. In the research described here, we prepared a self-healing acrylic acid-functionalized metallocene polyethylene elastomer (mPE-g-AA) nanocomposite with the addition of arginine to form supramolecular hydrogen bonding. Thermal characterization, mechanical properties, shape memory effect, and self-healing properties were investigated. The addition of mutilwall carbon nanotubes (MWCNTs) effectively increased the tensile properties of the modified mPE. The acrylic acid-modified mPE greatly improved its shape recovery ratio, up to 94.2 +/- 4.7%, and maintained a high shape fixing ratio (91.6 +/- 1.3%) due to the hydrogen bonding acting as physical crosslinks. Overall, all modified mPE samples showed good shape memory performance. Besides the conventional thermal heating to heal the scratched surface cracks, MWCNTs were incorporated to permit healing the surface cracks through near-infrared radiation (NIR). However, the MWCNTs-filled samples under the thermal healing process unexpectedly resulted in the crack widths increasing, perhaps due to the effect of the MWCNTs with high recovery stress pushing outward on both sides of the crack during heating. Interestingly, the synergistic approach of combining thermal healing and NIR was found to be the most effective in improving the healing efficiency of the mPE-g-AA-Arg/MWCNTs, close to 50% within a short time, in comparison with the existing literature with required healing times of 60 min to have a self-healing efficiency of 45% for mPE modified with maleic anhydride and 3-amino-1,2,4-triazole. To the best of the authors' knowledge, no work has been reported on the preparation of self-healing thermoplastic elastomer nanocomposites through this approach so far.