By using a graphics processing unit-accelerated parallel algorithm on a compute unified device architecture platform, we perform large-scale molecular dynamics simulations in a Lennard-Jones system to observe the entire crystallization process, including metastable stage, critical nuclei formation, and the stage of crystal growth. Although the intermediated precursors that play a role in determining the polymorphs are predominantly bcc ordered, the polymorph selection is rather different at different stages. The precursors that have a relatively high orientational order will be on average in a denser region than uniform liquids, but microscopically the crystal nucleation happens without a density change. The average density of nuclei first increases significantly, and then almost keeps independent on the crystallite size after the growing post-critical nucleus becomes large enough. With such a large enough system, the crystal growth rate is able to be calculated directly by doing a linear fit to the temporal evolution of growing crystallite size. The obtained value of the growth rate indicates that the actual crystal growth in the Lennard-Jones system where the crystal-liquid interface has several kinds of structures is possibly driven by both collision-controlled and diffusion-controlled mechanisms.