Adsorption of small molecules on waved graphene is greatly enhanced. Strong physical adsorption in the trough of waved graphene can be achieved by tuning the curvature. Chemical adsorption is on the crest of waved graphene. Exothermic dissociation of H2 and O2 can be realized on waved graphene under high compression. Wave graphene can be candidates as catalysts and gas storage/sensor.