Detailed molecular mechanism of polymer crystallization into the chain folded lamella is investigated by molecular dynamics simulation. Though the crystallization of polymer is generally a very slow process that seems to defy every computational approach, simplifications of the computational model are found to improve the computational efficiency and to accelerate the crystallization itself. A relatively short polymer model made up of 500 beads connected by harmonic springs is adopted here, and in addition the polymer is assumed to be strongly adsorbed on the growth surface. It is shown that the polymer molecule crystallizes into a neat chain folded lamella within several nanoseconds. The crystallization process is found to be divided into three I stages : the initial stage for the local chain ordering into small clusters, the intermediate stage for the coalescing of the clusters into small lamellae, and the late stage for the completion of a single lamella. In the crystallization process of our model polymer, the polymer diffusion along the chain and the subsequent lamella thickening are found to be of great significance. The thickening phenomena of our model lamella is also investigated, and it is found that the lamella thickens rather quickly, driven mainly by the van der Waals attraction between beads.