A battery replacement robot with a mobile storage rack includes a mechanical part and an electrical control part. The electrical control part controls a battery replacement device to place, in one step, all battery boxes required by one side of an electric bus that needs battery replacement onto a battery box storage rack. A horizontal moving unit moves to a position where a battery needs to be replaced. A battery box replacement device takes down a spent battery box from the electric bus; the battery box replacement device rotates towards one side around a Y axis, and raises or lowers the spent battery box so as to put the spent battery on the battery box storage rack; then the battery box replacement device takes down a charged battery box from the battery box storage rack, rotates to the original position, and installs the battery box in the electric bus.