Provided is a high-strength steel sheet that has good chemical convertibility and good corrosion resistance after electro deposition painting despite high Si and Mn contents. Also provided are a method for producing the high-strength steel sheet, a high-strength galvanized steel sheet formed by using the high-strength steel sheet, and a method for producing the high-strength galvanized steel sheet. A steel sheet containing, in terms of % by mass, C: 0.03 to 0.35%, Si: 0.01 to 0.50%, Mn: 3.6 to 8.0%, Al: 0.001 to 1.00%, P≤0.10%, S≤0.010%, and the balance being Fe and unavoidable impurities is annealed under condition under which a dew point of an atmosphere in a temperature zone of 550° C. or higher and A° C. or lower (A is a particular value that satisfies 600≤A≤750) inside an annealing furnace is controlled to −40° C. or lower.