We investigate the molecular mechanism of secondary nucleation on a growth surface of the polymer crystal. We adopt a simplified model of polyethylene molecule made of 500 beads connected by springs, and consider the crystallization from a vapor phase neglecting surrounding molecules. A strongly collapsed chain in a vacuum is placed near the infinitely wide lateral surface of the polymer crystal, and the molecular processes of adsorption and ordering are investigated by molecular-dynamics simulation. It is found that the polymer chain is quickly adsorbed, in a stepwise manner, to form a layer structure : A multilayered at lower temperature and a monolayered at higher temperature. The chain segments adsorbed to the surface align parallel with each other and gradually, within several ns, grow into a neat chain folded lamella with predominantly adjacent-reentry folds. The thickness of the lamella sensibly depends on the crystallization temperature and shows a rapid increase around the melting point. It is found that the polymer ordering on the surface is not a sequential process from the chain-end but a rather cooperative process of many segments. Furthermore, we investigate the effect of finite thickness of the substrate crystal, and find that the Limited thickness of the substrate gives rise to the frequent generation of chain loops at and the segregation of chain entanglements toward the lamella surfaces.