The main attraction of metallic nanolayered composites (MNCs) lies not only with their five-to ten-fold increases in strength over that of their constituents, but also in the tunability of their superior strength with nanolayer thickness. While the size scaling in strength prevails in many MNC material systems, the size scaling cannot be accurately predicted with crystal plasticity framework. Here, we present a crystal plasticity based computational method that considers plasticity to occur in grain boundary-controlled discrete slip events and apply it to predict the deformation response and underlying mechanisms in Cu/Nb MNCs. Predicted tensile stress-strain responses are shown to achieve agreement with measurements for four distinct nanolayer thicknesses, without introducing adjustable parameters. The model predicts the Hall-Petch size scaling of strength on layer thickness and the rising plastic anisotropy as the layer thickness reduces. Analysis of the results indicates that the origin of the layer size effect on strength results from the limits layer thickness places on the lengths of dislocations sources lying in the grain boundaries.