Laminated metals have the potential for achieving better mechanical properties, such as higher strength, ductility, and work hardening ability. The mechanism that leads to these advances stems from the inhomogeneous plastic deformations between soft and hard components where geometrically necessary dislocations (GNDs) are produced while the two adjacent components are mutually constrained. Many structural factors have already been extensively investigated during the optimization of the laminated structure, such as the effect of layer thickness and the strength differential between components on the overall resulting properties. However, the effect of component composition percentage, an important factor for laminated structures, on the mechanical properties and its underlying mechanism remains elusive. To unravel the effect of component composition percentage on the mechanical properties, we used stable nanotwinned structures as components to build laminated nanotwinned (LNT) Cu materials. Three LNT Cu samples with hard components on the surface layers and soft components in the core layer were designed and prepared by direct-current electrodeposition. The soft component percentages were set as 10%, 50%, and 90%. The mechanical behaviors of LNT Cu were explored by uniaxial tensile tests at room temperature. Yield strengths for all three LNT Cu were higher than that estimated by the rule of mixture, indicating an extra strengthening effect from the LNT structure. The LNT Cu containing 50% soft component (LNT-50%) demonstrated the greatest extra strengthening. Interestingly, full-field strain measurements and microstructure characterizations further indicated that the strain localization of LNT-50% was well suppressed and the lateral strain difference between the soft and hard components was obviously reduced. This indicated that the strong mutual constraint between the two components contributed to the greatest extra strengthening.