Abstract Nanotwinned metals with a gradient microstructure have attracted a great deal of attention due to their excellent mechanical performance of combining high strength and high ductility. In this work, a micromechanical model is developed to describe the stress-strain response of gradient-nanotwinned metals with a composite microstructure. The deformation mechanisms originated from bimodal grain size distribution in nanostructured materials and nanoscale twin lamellae in a grain are involved in derivation of flow stress. The contributions from the gradient distribution of microstructural size and the microcracks during plastic deformation are taken into account in simulating the mechanical properties such as the yield strength and ductility. Using the proposed model, we figure out the stress-strain relation of gradient nanostructured metals and analyze the quantitative relation between the mechanical properties and the geometrical/physical parameters related to the gradient-nanotwinned composite copper. Numerical results show that, the strength and ductility of the gradient-nanotwinned bimodal metals are both improved as twins spacing decreases. With the volume fraction of coarse-grained phase decreased, the strength is improved significantly accompanied by slight reduction of the ductility. In addition, the simulated results are in a good agreement with experimental results. The present work could be helpful to describe and predict the elastic-plastic deformation behavior of gradient nanostructured composite -metals.