This study uses molecular dynamics simulations to investigate the crystalline process of Co-Cu nanoparticles of high and low Co concentrations (5 and 25%) during the annealing process. The modified many-body tight-binding potential involving magnetic contribution is adopted to accurately model the Cu-Cu, Co-Co, and Co-Cu pair interactions. The Co-Co bond length increases, while the Co-Cu bond length decreases as the temperature gradually drops from 2000 K to the upper melting point. During that process, the Cu-Cu bond length remains constant and the value of the first peak of the radial distribution function (RDF) increases, which indicates that Cu atoms increase their short-range order by mutual rearrangement. At temperatures lower than the upper melting point, the bond length of each pair decreases while the value of the first peak increases as the temperature is continuously reduced. Because the kinetic energy of an individual atom is not enough for rearrangement, the variations of bond length and the first RDF peak can be attributed to the shrinking effect.