The effects of grain size on the deformation mechanisms of nano-polycrystal Cu and dual-phase nanostructured Cu/CuZr composites under tensile loading are studied by molecular dynamics method. The results show that for nano-polycrystal Cu with small grain size, the deformation mechanism is mainly dominated by grain rotation and grain boundary migration, accompanied by the nucleation and emission of a few dislocations. For nano-polycrystal Cu with large grain size, the plastic deformation mechanism is mainly dominated by the nucleation and growth of cracks. However, for the dual-phase nanostructured Cu/CuZr composites, the plastic deformation of amorphous phase plays a dominant role during plastic deformation, regardless of grain sizes. In addition, when the grain size becomes large, the grain boundary cracks also appear at the grain boundary of the composites, but the amorphous phase obviously hinders the nucleation and propagation of the cracks. The research shows that the introduction of amorphous phase can effectively enhance the plasticity of nano-polycrystal Cu.