Disclosed is a cooling member mounted at a top and/or a bottom of a battery module or a battery pack to remove heat generated from battery cells during charge and discharge of the battery cells, wherein the cooling member includes a thermal conduction member including a stepped fastening plate having step portions of different lengths, coolant flow channels being formed at interfaces of the fastening plate and a coolant conduit configured to have a hollow structure through which a coolant flows, the coolant conduit including a main conduit and one or more branch conduits extending vertically in a state in which the branch conduits communicate with the main conduit such that the branch conduits communicate with the coolant flow channels of the thermal conduction member.