Bimetallic core-shell nanoparticles such as NiCu are of great interest not only due to their excellent stability, selectivity, and magnetic and catalytic properties, but also because they are tunable by changing the morphology, surface element distribution, and particle size of the nanoparticles. The surface segregation and structural features of NiCu bimetallic nanoparticles, the deposition growth and the surface diffusion of Cu adsorbed atoms on the Ni substrate surface are studied by using molecular dynamics and the Montero method combined with embedded atomic potential. The results show that the Cu atom has a strong tendency of surface segregation. With the increase of concentration of Cu atoms, Cu atoms preferentially occupy the vertex, edge, (100), and (111) facet of nanoparticles due to the difference in configuration energy between Cu atoms and surface Ni atoms with different coordination numbers after the exchange, and finally form perfect Ni-core/Cu-shell nanoparticles. When growth temperature T = 400 K, the Ni-core/Cu-shell structure formed is the most stable. By observing the NiCu core-shell structure’s growth sequence, it is found that a few Ni atoms are replaced by Cu atoms on the step edge of the Ni substrate. The diffusion energy barrier of Cu atoms adsorbed on a Ni substrate surface is calculated by using the nudged elastic band method. The results show that Cu atoms adsorbed need to overcome a large ES barrier for both exchange and diffusion, making it difficult to diffuse between the facets of Ni substrate surface in a temperature range of 200–800 K. The lowest energy barrier for the diffusion of Cu atoms between facets of Ni substrate surface is 0.43 eV, and the diffusion path is from (111) facet to (100) facet. In contrast to Ni substrate, Ni atoms deposited on Cu substrate can easily migrate from the (111) facet to the (100) facet with a diffusion energy barrier of only about 0.12 eV, and at the present simulated temperature, Ni adsorbed atoms are unable to migrate on the (100) facet, resulting in a growth configuration toward an octahedral shape with its eight apex angles almost occupied by Ni atoms. In this paper, a new idea and method are provided for the preliminary design of NiCu nano-catalysts from atoms.