Molecular dynamics simulation with a coarse grain model is performed to study the influence of single nanoparticle on the polymer crystallization behavior. By changing the mode of action of the polymer-nanoparticle (i.e. attraction or repulsion), the strength of the polymer-nanoparticle interactions, as well as the chain length of the polymer molecular, and by calculating the bond order parameter to characterize the influence in the cooling process, different effects of single nanoparticle on the polymer crystallization behavior are studied. This study has shown that the nanoparticle has no obvious effect on the whole polymer system composed of single nanoparticles. However, nanoparticles can promote the degree of order of polymer chains in crystallization process and enhance partially the polymer crystallization. Under the attraction and strong strength of the polymer-nanoparticle interaction, it is found that obviously the nanoparticle enhances the polymer crystallization partially. Furthermore, the chain length of the polymer molecular also shows some effect on the crystallization and the long-chain sample has a better enhancement for the polymer crystallization than the short-chain one under a strong attraction strength.