Gradient nanostructured (GNS) metals exhibit high overall extra strengths relative to their non-gradient counterparts. However, the spatial distribution of local extra strengths stemming from plastic strain gradients remains elusive. This work is focused on characterizing the gradient distribution of plastic strains in a representative GNS metal of gradient nanotwinned (GNT) Cu. Full-field strain mapping reveals the gradient distributions of lateral strains in the transverse cross section of GNT Cu samples undergoing uniaxial tensile deformation. We find that the lateral strain gradient increases but the maximum lateral strain difference decreases in GNT samples with increasing structural gradient. The latter arises because the softest layer with the lowest initial yield strength gains the largest local extra strength during tensile deformation, and vice versa. Such a gradient distribution of local extra strengths results from the combined strengthening effects of plastic strain gradient and grain size. These experimental results are used to inform a strain gradient plasticity model for revealing the gradient distributions of local extra back stresses and local extra strengths with increasing load. The coupled experimental and modeling characterization of gradient plastic deformation provides an in-depth mechanistic understanding of the spatial-temporal evolution of gradient strengthening effects in gradient nanostructures.