Shapes and structures of seeds are critically important for the seed-mediated synthesis of anisotropic nanostructures. By the deposition of Cu atoms on different Au seeds, Cu nanostructures of different shapes could be synthesized. In experiments Cu nanorods formed with Au nanobipyramids as seeds, and the growth of Cu nanorods was studied through a series of experiments. It is found that the growth direction Cu nanorod is along the penta-twinned axis of Au nanobipyramids and bound by {200} side facets. For the case of low Cu 2+ concentration in reaction system, Cu atoms would prefer to deposit on one end of Au nanobipyramids. Nevertheless, Cu atoms would deposit on two ends of Au nanobipyramids for the case of high Cu 2+ concentration. Due to the different deposition and migration rates of Cu atoms at two ends of Au nanobipyramids, the Cu nanorods products exhibited different morphologies. Similarly, Cu nanopolyhedrons and Cu nanocubiods were synthesized with Au nanospheres and nanorods as seeds, respectively. Our work is of great significance for further fundamental research and applications of the Cu nanostructure-based nanomaterials in catalytic and electronic fields.