An oxygen scavenger comprises an oxygen absorbent composition and an oxygen permeable film covering the oxygen absorbent composition and including an asymmetric porous membrane whose outer surface portion in the thickness direction of the asymmetric porous membrane is formed as a dense skin layer. Since the dense skin layer is very thin, the oxygen permeability to the oxygen absorbent composition through the oxygen permeable film can be maintained sufficiently high. At the same time, since the dense skin layer has a sufficiently high barrier property as well as a high oxygen permeability, contact of the substances stored in a container with the oxygen absorbent composition can be surely prevented. The substances stored in the container attached with the oxygen scavenger can be prevented from deterioration due to the oxygen present in the container by a high oxygen absorption ability of the scavenger, and maintained in a good or fresh condition for a long term.