Disclosed is a method of producing a hot-dip galvanized steel sheet with excellent surface appearance, coating adhesion, and corrosion resistance. A method of producing a hot-dip galvanized steel sheet disclosed herein includes: performing first annealing comprising holding a steel sheet having a chemical composition containing, in mass%, Si: 0.10 % or more and 3.0 % or less and Mn: 1.0 % or more and 10.0 % or less within a temperature range of 650 °C to 900 °C for 30 seconds or more in a reducing atmosphere containing hydrogen and having a dew point of -65 °C or higher and -20 °C or lower, and then cooling the steel sheet; then forming, on a surface of the steel sheet, an Fe coating with a coating weight of 0.3 g/m² or more and 10.0 g/m² or less; then performing second annealing comprising holding the steel sheet within a temperature range of 700 °C to 900 °C for 30 seconds or more in a reducing atmosphere containing hydrogen and having a dew point of 0 °C or lower, heating the steel sheet to a maximum arrival temperature of 900 °C or lower, and then cooling the steel sheet; and then applying a hot-dip galvanized coating onto the steel sheet.