A system for inspecting quality of a membrane-electrode assembly (MEA) of a fuel cell includes a bonding device configured to bond the MEA and a gas diffusion layer (GDL) to manufacture a bonded unit thereof. A transfer device adsorbs one surface of the bonded unit to transfer the bonded unit. An inspection device is disposed on one side of the bonded unit transferred by the transfer device and inspects an outer appearance of the bonded unit. A reversing device places the bonded unit thereon by the transfer device and reverses the bonded unit vertically. A loading and lifting device loads the bonded unit thereon after being transferred by the transfer device and adjusts a loading height.