Nanotwinned materials not only exhibit high strength but also possess substantial ductility. Their fatigue properties and damage behavior of materials are also attractive for material scientist. However, fully reversed tension-compression fatigue tests on nanostructued materials under strain and stress control have not been carried out yet, mainly owing to the limitation of the sample thickness. In this study, real bulk polycrystalline Cu samples with preferentially oriented nanoscale twins were synthesized by means of direct current electrodeposition technique. Tension-compression fatigue tests were performed on the bulk nanotwinned Cu samples under constant strain controlled and stress controlled fatigue tests, respectively. The cyclic stress/strain response, strain-controlled low-cycle fatigue life as well as high-cycle fatigue limit under stress control were explored. The underlying cyclic stress/strain response associated with the effect of microstructure features, including TB orientation, twin thickness and twin lamellar length (i.e. grain size), were discussed.