A honeycomb structure having a periphery and two ends, including a plurality of passages which are defined by partition walls and extend in an axial direction between the ends, wherein the partition walls are formed of a plurality of through holes for forming turbulent flow so that the fluid pass through the through holes from one of the passages to the adjacent passage, each of the through holes having an open area of at least 0.25 mm.sup.2, thereby a stream of the fluid passing through the honeycomb structure is efficiently mixed to increase its contact with a catalyst composition coated on a surface of the partition walls. The honeycomb structure may have a corrugated thin metal foil. Alternatively, the honeycomb structure may have a unitary structure formed by sintering an extruded body comprising a powder material. A heater for heating fluid flowing therethrough, has the honeycomb structure being electrically conductive and an electrode for applying electric current to the honeycomb structure so as to generate heat.