Nanotwinned copper (nt-Cu) shows a broad application prospects as interconnection materials in integrated circuit industry, since it combines the excellent mechanical and electrical properties. However, the formation and growth behavior of twin lamellae in pulse electrodeposited copper films are not fully understood. In this work, a series of electroplated copper films are prepared by verifying the electroplating parameters and the microstructures are analyzed using scanning electron microscope (SEM) and transmission electron microscope (TEM). The surface morphology indicates strong evidence of stacked twin terraces and layers, suggesting that nanotwins grow up layer by layer. Combined with in situ characterization by SEM and molecular dynamics (MD) simulation, it is proved that the terraces originate from the triple junction of grain boundaries and grow up by extending along the lateral (111) crystal plane. A twin terrace-growing model for nt-Cu is then deduced, which distinguishes from deformation twins or annealed twins. This growth model would be prospective to help obtain high quality of nt-Cu in industry.