A gas supply connector of the present invention includes a gas supply member and two fasteners, wherein the gas supply member has a main body and multiple tubes; the fastener includes a buckling portion, a pressing portion and a neck portion. The pressing portion has an inner layer body and an outer layer body. The neck portion contracts from two lateral ends toward the center to form a tapered section, and the outer surface of the neck portion is arranged with multiple reinforcing ribs. The present invention through the neck portion reduces the force required for pressing the fastener to deform by the user, and through the reinforcing ribs increases the structural strength of the neck portion to prevent the fastener from breaking; in addition, the inner layer is made of plastic, and outer layer body is made of soft material, so as to improve the comfort of pressing fastener.