A continuous annealing furnace for annealing steel strips that is a vertical-type annealing furnace is configured so that part of gas inside the furnace is drawn and introduced to a refiner disposed outside the furnace including an oxygen removing apparatus and a dehumidifying apparatus, oxygen and moisture contained in the gas are removed to lower the dew point of the gas, and the gas having a lowered dew point is put back into the furnace. At least one gas inlet through which gas is drawn from the furnace into the refiner is disposed in the vicinity of the entry side of the furnace at a distance of 6 m or less in the vertical direction and 3 m or less in the furnace-length direction from the steel-strip-introduction section located at the lower part of the heating zone.