The invention relates to a packaging structure of an energy storage device. At least one unit cell of capacitor is stacked and packaged into the energy storage device. The unit cell is a sandwich structure comprising a solid-state polymer electrolyte between two modified carbonaceous electrodes. An assembly of at least one unit cell of capacitor can be packaged by metallic cases to form a coin cell type or screw type of the packaging structure, packaged with a plastic case by compression molding or injection molding, or packaged by a plastic bag or an aluminum-foil bag and sealed by heat sealing or vacuum heat sealing. Manufacture processes for traditional capacitor modules, such as drilling, welding, screwing, and making scaffolds, are not required. Although the packaging process is simpler and less expensive, the packaged energy storage device can perform better than traditional capacitor modules.