A method of producing a galvannealed steel sheet using a continuous hot-dip galvanizing device that includes: an annealing furnace in which a heating zone including a direct fired furnace, a soaking zone, and a cooling zone are arranged in the stated order; a hot-dip galvanizing line adjacent to the cooling zone; and an alloying line adjacent to the hot-dip galvanizing line, the method comprising: annealing a steel strip having a Si content of 0.2 mass% or more by conveying the steel strip through the heating zone, the soaking zone, and the cooling zone in the stated order in the annealing furnace; applying a hot-dip galvanized coating onto the steel strip discharged from the cooling zone, using the hot-dip galvanizing line; and heat-alloying the galvanized coating applied on the steel strip, using the alloying line, wherein reducing gas or non-oxidizing gas is supplied into the soaking zone, the reducing gas or the non-oxidizing gas including: mixed gas obtained by mixing gas humidified by a humidifying device and gas not humidified by the humidifying device at a predetermined mixture ratio; and dry gas not humidified by the humidifying device, the mixed gas is timely supplied into the soaking zone from at least one mixed gas supply port (36A, 36B, 36C, 38A, 38B, 38C) located in a region of lower 1/2 of the soaking zone in a height direction, and the dry gas is timely supplied into the soaking zone from at least one dry gas supply port (40A, 40B, 40C) located at or in a range of 2 m lower than a center of an upper hearth roll in the soaking zone in the height direction, and furnace gas is timely discharged from the soaking zone through at least one gas discharge port (42A, 42B) located higher than the upper hearth roll, to control a dew point in at least an uppermost part of the soaking zone to -20 °C or more and 0 °C or less. annealing a steel strip having a Si content of 0.2 mass% or more by conveying the steel strip through the heating zone, the soaking zone, and the cooling zone in the stated order in the annealing furnace; applying a hot-dip galvanized coating onto the steel strip discharged from the cooling zone, using the hot-dip galvanizing line; and heat-alloying the galvanized coating applied on the steel strip, using the alloying line, wherein reducing gas or non-oxidizing gas is supplied into the soaking zone, the reducing gas or the non-oxidizing gas including: mixed gas obtained by mixing gas humidified by a humidifying device and gas not humidified by the humidifying device at a predetermined mixture ratio; and dry gas not humidified by the humidifying device, the mixed gas is timely supplied into the soaking zone from at least one mixed gas supply port (36A, 36B, 36C, 38A, 38B, 38C) located in a region of lower 1/2 of the soaking zone in a height direction, and the dry gas is timely supplied into the soaking zone from at least one dry gas supply port (40A, 40B, 40C) located at or in a range of 2 m lower than a center of an upper hearth roll in the soaking zone in the height direction, and furnace gas is timely discharged from the soaking zone through at least one gas discharge port (42A, 42B) located higher than the upper hearth roll, to control a dew point in at least an uppermost part of the soaking zone to -20 °C or more and 0 °C or less.