A method of fabricating a product of activated carbon fiber supporting silver has the steps of: a) Impregnate activated carbon fibers in a silver acetate solution under a vacuum condition for a predetermined time to deposit silver on surfaces of the activated carbon fibers via a chemical reaction. And then, dry the activated carbon fibers to remove water therein. b) Heat the activated carbon fibers in a stove filled with protective gas to break the silver on the activated carbon fibers into very fine grains, and c) wash the activated carbon fibers to remove redundant sliver from the surfaces of the activated carbon fibers.