A catalytic combustion heater for a heat exchanger (1) which has a fuel gas flow passage (11), and a plurality of tubes (5) provided in the fuel gas flow passage, formed so as to have a fluid to be heated flow therein, and having catalyst support fins (51) fixed to an outer surface thereof, and which is formed so that the object fluid is heated by an oxidation reaction of the fuel gas. A control unit (6) is adapted to judge that a flow rate of the object fluid is low until the temperature of the object fluid detected by temperature detector (8) provided in the vicinity of an outlet of an object fluid flow passage (55) has not exceeded a predetermined level, for example, a boiling point thereof, to restrain the heat transfer to the interior of the tubes (5) and increase temperature of the fins (51) early to a catalyst activating level. Said control unit is also adapted to increase the flow rate of the object fluid to a specific level after the temperature thereof has exceeded the boiling point thereof, to promote the heat transfer to the object fluid, whereby a desired high-temperature gas is obtained with a short starting time as the attainment of unnecessarily high temperatures of the fins (51) and tubes (5) is prevented.