The present invention prevents readily oxidizable elements contained in a steel, such as Si and Mn, from concentrating in the surface of a steel strip during annealing and thereby forming oxides of the readily oxidizable elements. Use is made of a vertical annealing furnace which is equipped with a heating zone, a soaking zone, and cooling zones and in which part of the furnace gas is introduced into a refiner disposed outside the furnace and is reduced in dew point therein and the gas having a lowered dew point is returned to the furnace. A part which connects the soaking zone and the cooling zones is disposed in the upper part of the furnace. Withdrawal ports for the furnace gas to be introduced into the refiner are disposed respectively in the cooling zone which is located in the vicinity of the part that connects the soaking zone and the cooling zones and in the upper part of the soaking zone. Injection ports for the furnace gas returning from the refiner are disposed respectively in the part that connects the soaking zone and the cooling zones and in the lower part of the soaking zone. The annealing furnace is configured so that the rate of gas withdrawal (Qo1) from the cooling zone which is located in the vicinity of the part that connects the soaking zone and the cooling zones, the rate of gas withdrawal (Qo2) from the upper part of the soaking zone, the rate of gas injection (Qi1) into the part which connects the soaking zone and the cooling zones, the rate of gas injection (Qi2) into the lower part of the soaking zone, the rate of surrounding-gas feeding (Qf1) to the cooling zones and to the subsequent zone, the rate of surrounding-gas feeding (Qf2) to the soaking zone, the internal volume (Vs) of the soaking zone, and the average temperature (Ts) of the soaking zone satisfy relationships, e.g., 0.3 * Qf1 < Qo1.