A battery module having a plurality of stacked battery module units is provided. The battery module unit includes a cooling fin in which an interval between two cooling plates facing each other is expandable and contractible. A battery cell is in contact with each of the two cooling plates and having lead tabs at each end. Protruding steps extend from both ends of the cooling plates to maximize a contact area with the lead tabs of the battery cell. Lead tab fasteners are coupled to the protruding steps to fix the lead tabs of the battery cell to the protruding steps. The lead tap fasteners include connecting grooves and connecting protrusions relative to each other to be coupled by a linear relative movement with lead tap fasteners of an adjacent battery module unit.