A method for producing a high-strength galvanized steel sheet, the method comprising: using a steel sheet containing a chemical composition, in mass%, C: 0.3% or less, Si: 0.1 to 2.5%, Mn: 0.5 to 3.0%, P: 0.100% or less, and S: 0.0100% or less, and optionally at least one of Al: 0.01 to 0.1%, Mo: 0.05 to 1.0%, Nb: 0.005 to 0.05%, Ti: 0.005 to 0.05%, Cu: 0.05 to 1.0%, Ni: 0.05 to 1.0%, Cr: 0.01 to 0.8%, B: 0.0005 to 0.005%, Sb: 0.001 to 0.10%, and Sn: 0.001 to 0.10% with a balance of Fe and incidental impurities; performing oxidation processing on the steel sheet; thereafter performing reduction-annealing on the steel sheet; and thereafter performing hot-dip galvanizing processing on the steel sheet, wherein the oxidation processing is performed in such a manner that, in a first stage, the steel sheet is heated at a temperature of 400 to 750°C in an atmosphere having an O 2 concentration of 1000 ppm by volume or more and a H 2 O concentration of 1000 ppm by volume or more, and, in a second stage, the steel sheet is heated at a temperature of 600 to 850°C in an atmosphere having an O 2 concentration of less than 1000 ppm by volume and a H 2 O concentration of 1000 ppm by volume or more, and the reduction-annealing is performed in a reduction-annealing furnace in such a manner that, in a heating zone of the furnace, the steel sheet is heated at a heating rate of 0.1°C/sec or more to a temperature of 650 to 900°C in an atmosphere having a H 2 concentration of 5 to 30 vol % and a H 2 O concentration of 10 ppm by volume or more and less than 500 ppm by volume with a balance of N 2 and incidental impurities, and thereafter, in a soaking zone of the furnace, the steel sheet is soaked and held for 10 to 300 seconds with a temperature variation in the soaking zone of ±20°C or less in an atmosphere having a H 2 concentration of 5 to 30 vol % and a H 2 O concentration of more than 1000 ppm by volume and 5000 ppm by volume or less with a balance of N 2 and incidental impurities. using a steel sheet containing a chemical composition, in mass%, C: 0.3% or less, Si: 0.1 to 2.5%, Mn: 0.5 to 3.0%, P: 0.100% or less, and S: 0.0100% or less, and optionally at least one of Al: 0.01 to 0.1%, Mo: 0.05 to 1.0%, Nb: 0.005 to 0.05%, Ti: 0.005 to 0.05%, Cu: 0.05 to 1.0%, Ni: 0.05 to 1.0%, Cr: 0.01 to 0.8%, B: 0.0005 to 0.005%, Sb: 0.001 to 0.10%, and Sn: 0.001 to 0.10% with a balance of Fe and incidental impurities; performing oxidation processing on the steel sheet; thereafter performing reduction-annealing on the steel sheet; and thereafter performing hot-dip galvanizing processing on the steel sheet, wherein the oxidation processing is performed in such a manner that, in a first stage, the steel sheet is heated at a temperature of 400 to 750°C in an atmosphere having an O 2 concentration of 1000 ppm by volume or more and a H 2 O concentration of 1000 ppm by volume or more, and, in a second stage, the steel sheet is heated at a temperature of 600 to 850°C in an atmosphere having an O 2 concentration of less than 1000 ppm by volume and a H 2 O concentration of 1000 ppm by volume or more, and the reduction-annealing is performed in a reduction-annealing furnace in such a manner that, in a heating zone of the furnace, the steel sheet is heated at a heating rate of 0.1°C/sec or more to a temperature of 650 to 900°C in an atmosphere having a H 2 concentration of 5 to 30 vol % and a H 2 O concentration of 10 ppm by volume or more and less than 500 ppm by volume with a balance of N 2 and incidental impurities, and thereafter, in a soaking zone of the furnace, the steel sheet is soaked and held for 10 to 300 seconds with a temperature variation in the soaking zone of ±20°C or less in an atmosphere having a H 2 concentration of 5 to 30 vol % and a H 2 O concentration of more than 1000 ppm by volume and 5000 ppm by volume or less with a balance of N 2 and incidental impurities.