An adsorbent structure including a honeycomb structure having a periphery and two ends, the honeycomb structure having a plurality of passages which are defined by partition walls and extend in an axial direction between the ends, and a composition including zeolite coated on the partition walls. The zeolite may be a high-silica zeolite having a Si/Al ratio of not less than 40. The composition may include a mixture of zeolite and heat-resistant oxide loaded with a noble metal, and the zeolite may also be loaded with a noble metal. Further, the composition may include two layers, a first layer comprising zeolite, and a second layer comprising a heat-resistant oxide loaded with a noble metal. The first layer comprising zeolite may be loaded with a noble metal.