An ATM switching apparatus applicable to a short cell including an ATM-SW outputting a cell from an output path corresponding to a cell identifier, an interface unit, a demultiplexer, and a multiplexer. The interface unit sets, when a cell storing a plurality of short cells is inputted, the cell identifier so that the cell is transmitted from ATM-SW to the demultiplexer, and outputs the cell toward the ATM-SW. The demultiplexer receives the cell and produces a plurality of partial fill cells, and outputs them, while setting an identifier of each partial fill cell, the partial fill cell is outputted. The multiplexer receives a plurality of the partial fill cells, produces a cell storing a plurality of the short cells in accordance with the identifiers and outputs the cell to the ATM-SW.