Molecular dynamics simulations are carried out on the isothermal crystallization process of single polyethylene chains with different chain lengths on the single wall carbon nanotube. This process is summarized as two steps, i.e., adsorption and orientation, and the bond-orientational order parameter is used to show the details of this process. The results show that the attractive van der Waals interactions control the adsorption and orientation of polyethylene on single wall carbon nanotube, and as the chain length increases, more microstructures appear in the last ordered structure. The stems of the ordered structure align parallel to the single wall carbon nanotube axis.