Plastic pre-strain may decrease the yield strength of metallic materials when stressed in the opposite direction, known as Bauschinger’s effect, which could considerably influence the performance of the materials during cyclic loading processes such as fatigue and fretting. In this study, effects of twin boundary (TW) as an ordered obstacle in a nanoscaled Cu crystal on defects’ generation and annihilation during cyclic tension–compression loading processes were investigated, in comparison with those occurring in a single crystal (SC), using a molecular dynamics simulation technique. It was observed that the Bauschinger’s effect in the nanoscaled TW system was weaker with higher residual strain energy, compared to the SC system; and, the ductility of both the SC and TW systems was increased by the cycling loading, but this increase was smaller for the TW system. Efforts were made to elucidate the mechanisms involved.