The present invention addresses the problem and purpose of providing a honeycomb structure that has a sufficiently high strength and is excellent in endurance, and a catalyst for cleaning an exhaust gas using the same that is excellent in resistance to sulfur oxide (SOX). The honeycomb structure of the present invention is one consists of a flat inorganic fiber sheet comprising an inorganic fiber sheet having supported thereon an inorganic binder and zeolite, and a corrugated inorganic fiber sheet comprising an inorganic fiber sheet having supported thereon the same inorganic binder and zeolite, which are alternately combined with each other, wherein it is characterized in that the zeolite has a particle diameter (i.e., a median particle diameter, D50) of from 0.5 to 10.0 µm.