In this study, texture modelling of a copper single crystal processed by accumulative roll-bonding (ARB) was conducted for the first time. A crystal plasticity finite element method (CPFEM) model was developed, and the predicated textures were validated by the experimental observations conducted by another research group. A heterogeneous through-thickness deformation was revealed. Two types of matrix bands formed through the thickness after the first ARB cycle, and different crystal rotation, slip system activation, and shear strain evolved in matrix bands. Due to the cutting, stacking and roll-bonding involved in ARB, transition of deformation behaviours has been found after a position being moved to a new position in the next cycle, and this transition was investigated based on the CPFEM model.