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 chemical composition comprising Si in a range 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 the steel strip is conveyed vertically a plurality of times inside the soaking zone, an average temperature in the soaking zone is 700 °C to 900 °C, reducing gas or non-oxidizing gas is supplied into the soaking zone, the reducing gas or the non-oxidizing gas is mixed gas obtained by mixing gas humidified by a humidifying device and dry gas not humidified by the humidifying device at a predetermined mixture ratio, the mixed gas is supplied into the soaking zone from at least one gas supply port located in a region of lower 1/2 of the soaking zone in a height direction so that a dew point measured in a region of upper 1/5 of the soaking zone in the height direction and a dew point measured in a region of lower 1/5 of the soaking zone in the height direction are both -20°C or more and 0°C or less, and a condition of supplying the mixed gas to the soaking zone satisfies the following Formula: [Math. 1] 2820 − m a − m b y a − y b y i Vt N ≤ m i V i ≤ 12120 − m a − m b y a − y b y i Vt N where "V" is a flow rate of the mixed gas in m 3 /hr, "m" is moisture content in the mixed gas calculated from a dew point of the mixed gas in ppm, "y" is a height position of a dew point meter or a gas supply port in m, "N" is a total number of the gas supply ports, subscript "t" is total mixed gas, subscript "a" is a dew point meter located in the region of upper 1/5 of the soaking zone in the height direction, subscript "b" is a dew point meter located in the region of lower 1/5 of the soaking zone in the height direction, and subscript "i" is an ith gas supply port. annealing a steel strip having a chemical composition comprising Si in a range 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 the steel strip is conveyed vertically a plurality of times inside the soaking zone, an average temperature in the soaking zone is 700 °C to 900 °C, reducing gas or non-oxidizing gas is supplied into the soaking zone, the reducing gas or the non-oxidizing gas is mixed gas obtained by mixing gas humidified by a humidifying device and dry gas not humidified by the humidifying device at a predetermined mixture ratio, the mixed gas is supplied into the soaking zone from at least one gas supply port located in a region of lower 1/2 of the soaking zone in a height direction so that a dew point measured in a region of upper 1/5 of the soaking zone in the height direction and a dew point measured in a region of lower 1/5 of the soaking zone in the height direction are both -20°C or more and 0°C or less, and a condition of supplying the mixed gas to the soaking zone satisfies the following Formula: [Math. 1] 2820 − m a − m b y a − y b y i Vt N ≤ m i V i ≤ 12120 − m a − m b y a − y b y i Vt N where "V" is a flow rate of the mixed gas in m 3 /hr, "m" is moisture content in the mixed gas calculated from a dew point of the mixed gas in ppm, "y" is a height position of a dew point meter or a gas supply port in m, "N" is a total number of the gas supply ports, subscript "t" is total mixed gas, subscript "a" is a dew point meter located in the region of upper 1/5 of the soaking zone in the height direction, subscript "b" is a dew point meter located in the region of lower 1/5 of the soaking zone in the height direction, and subscript "i" is an ith gas supply port. "V" is a flow rate of the mixed gas in m 3 /hr, "m" is moisture content in the mixed gas calculated from a dew point of the mixed gas in ppm, "y" is a height position of a dew point meter or a gas supply port in m, "N" is a total number of the gas supply ports, subscript "t" is total mixed gas, subscript "a" is a dew point meter located in the region of upper 1/5 of the soaking zone in the height direction, subscript "b" is a dew point meter located in the region of lower 1/5 of the soaking zone in the height direction, and subscript "i" is an ith gas supply port.