A battery system capable of cooling overheated battery packs among a plurality battery packs each mounted in a battery case by measuring temperatures of the battery packs is disclosed, and a driving method thereof is provided. In one embodiment, the battery system includes a plurality of battery packs, an air compressor for supplying a compressed cooling air to the plurality of battery packs, a gas dividing unit coupled between the plurality of battery packs and the air compressor and including a plurality of valves, and a controller for controlling opening and closing of each of the plurality of valves according to temperatures of the plurality of battery packs.