We report a template-induced preferential electrodeposition method for tailoring hexagonally packed metal hollow-nanocones and taper-nanotubes. After sputtering a layer of Au film, anodized aluminum foils with controllable periods and depths of taper-nanopore templates can be directly used as cathodes. Nanonipples on the top-layer of alumina taper-nanopores can cause the "tip effect" during electrodeposition, which makes the metal deposition rate far rapider at the surface of templates than that at the lateral walls and the bottom of nanopores. Accordingly, the pore opening of the template can be rapidly closed while their interior is still hollow. Based on this principle, ordered arrayed of hollow-nanocones with controllable periods (e.g., 100, 200, and 300 nm) and material composition (e.g., Ni, Fe, and Cu) can be realized in a simple, inexpensive, and accessible way. Besides, hexagonally packed metal taper-nanotubes can also be obtained by skillfully making use of the combination of both the "tip effect" and "self-masking" effect of relatively deeper (e.g., 576 nm) taper-nanopores during Au sputtering. Our work opens a door for studying the physical and chemical properties of hexagonally packed hollow-nanocones and tapered-nanotubes made of various metal materials.