The structural and mechanical properties of a commercial A5052 aluminum–magnesium alloy processed by accumulative roll bonding (ARB) and subsequent annealing were investigated. Unimodal and bimodal grain-structures were formed in the ARB-processed specimens by annealing at 250°C and 300°C, respectively. In the specimen ARB-processed and annealed at 300°C, {001}<100> cube orientation became the main texture component which corresponded to coarse recrystallized grains in the bimodal grain-structures. The preferential formation of the cube texture could be explained by existing theories regarding stored energy and grain boundary mobility. High strength and high ductility was both managed in the specimens with bimodal grain-structures as well as those with unimodal grain-structures. In order to achieve both high strength and high ductility in bimodal grain-structures, the area fraction of coarse grains to fine grains played a critical role. It was also suggested in this study that bimodal structures were not only the structure to provide the coexistence of high strength and high ductility.