A secondary battery with a finishing tape preventing air bubbles from being formed between a jelly roll electrode structure and the finishing tape. The secondary battery includes a wound electrode assembly having a positive electrode sheet, a separator, and a negative electrode sheet, sequentially stacked, and a finishing tape having penetrating holes and adhered to the outer lateral surface of the wound electrode assembly. The penetrating holes permit air to escape, preventing the formation of air bubbles under the tape. The secondary battery may be made by sequentially stacking a positive electrode sheet, a separator, and a negative electrode sheet to form an electrode structure, adhering a finishing tape to a surface of one of the positive and negative electrode sheets of the electrode structure, the finishing tape including penetrating holes, applying tension to a free end of the finishing tape and winding the electrode structure in a spiral with the finishing tape covering and adhered to the electrode structure as an outside surface, whereby air trapped between the electrode structure and the finishing tape during winding passes through the penetrating holes, preventing formation of air bubbles between the finishing tape and the electrode structure. Alternatively, the secondary battery may be made by sequentially stacking a positive electrode sheet, a separator, and a negative electrode sheet to form an electrode structure, winding the electrode structure in a spiral having an outside surface, and adhering a finishing tape including penetrating holes to the outside surface by winding the tape around the spiral, covering the outside surface and adhering the finishing tape to itself, so that air trapped between the electrode structure and the finishing tape during winding passes through the penetrating holes, preventing formation of air bubbles between the finishing tape and the electrode structure.