To make full use of the strength of carbon nanotubes in a composite, it is important to have a high-stress transfer at the matrix-nanotube interface via strong chemical bonding. This paper investigates the possible polyethylene-nanotube bonding with the aid of a quantum mechanics analysis. The polyethylene chains were represented by alkyl segments, and the nanotubes were modeled by nanotube segments with H atoms added to the dangling bonds of the perimeter carbons. The study predicts that covalent bonding between an alkyl radical and a nanotube is energetically favorable, and that the tubes of smaller diameters have higher binding energies. Hence, a high-stress transfer can be realized in polyethylene-based carbon nanotube composites in the presence of free-radical generators.