A method for producing high-strength galvanized steel sheets, comprising: a hot rolling step of obtaining a hot-rolled steel sheet, comprising hot rolling a slab, thereafter coiling the hot rolled slab into a coil at a temperature T C satisfying the relation below, which is followed by pickling, wherein the slab consists of, in mass%, C: 0.05 to 0.30%, Si: 0.1 to 2.0%, Mn: 1.0 to 4.0% and optionally one or more elements selected from 0.01 to 0.1% Al, 0.05 to 1.0% Mo, 0.005 to 0.05% Nb, 0.005 to 0.05% Ti, 0.05 to 1.0% Cu, 0.05 to 1.0% Ni, 0.01 to 0.8% Cr and 0.0005 to 0.005% B, the remainder being Fe and inevitable impurities, a cold rolling step of cold rolling the hot-rolled steel sheet resulting from the hot rolling step, an annealing step of annealing the cold-rolled steel sheet resulting from the cold rolling step wherein the annealing includes (zone-A heating) to (zone-C heating) described below, and a galvanizing step of galvanizing the annealed sheet resulting from the annealing step in a galvanizing bath containing 0.12 to 0.22 mass% Al; (zone-A heating) the cold-rolled steel sheet is heated in a DFF heating furnace at an air ratio α and an average heating rate at 200°C and above of 10 to 50°C/sec to a target heating temperature T 1 (°C) satisfying the relation below; (zone-B heating) the cold-rolled steel sheet resulting from the zone-A heating is heated in a DFF heating furnace at an air ratio ≤ 0.9 and an average heating rate at above T 1 of 5 to 30°C/sec to a target heating temperature T 2 (°C) satisfying the relation below; (zone-C heating) the cold-rolled steel sheet resulting from the zone-B heating is heated in an atmosphere containing H 2 and H 2 O, the balance being N 2 and inevitable impurities, at a log(P H2O /P H2) of not less than -3.4 and not more than -1.1 and an average heating rate at above T 2 of 0.1 to 10°C/sec to a prescribed target heating temperature T 3 (°C) of 700 to 900°C, and is held at T 3 for 10 to 500 seconds; T C ≤ − 60 Si + Mn + 775 T 1 ≥ 28.2 Si + 7.95 Mn − 86.2 α + 666 T 2 ≥ T 1 + 30 wherein [Si] and [Mn] are the contents of mass% Si and Mn present in the slab, α is not more than 1.5 and not less than 0.9, and log (P H2O /P H2) is log(H 2 O partial pressure (P H2O)/H 2 partial pressure (P H2)). a hot rolling step of obtaining a hot-rolled steel sheet, comprising hot rolling a slab, thereafter coiling the hot rolled slab into a coil at a temperature T C satisfying the relation below, which is followed by pickling, wherein the slab consists of, in mass%, C: 0.05 to 0.30%, Si: 0.1 to 2.0%, Mn: 1.0 to 4.0% and optionally one or more elements selected from 0.01 to 0.1% Al, 0.05 to 1.0% Mo, 0.005 to 0.05% Nb, 0.005 to 0.05% Ti, 0.05 to 1.0% Cu, 0.05 to 1.0% Ni, 0.01 to 0.8% Cr and 0.0005 to 0.005% B, the remainder being Fe and inevitable impurities, a cold rolling step of cold rolling the hot-rolled steel sheet resulting from the hot rolling step, an annealing step of annealing the cold-rolled steel sheet resulting from the cold rolling step wherein the annealing includes (zone-A heating) to (zone-C heating) described below, and a galvanizing step of galvanizing the annealed sheet resulting from the annealing step in a galvanizing bath containing 0.12 to 0.22 mass% Al; (zone-A heating) the cold-rolled steel sheet is heated in a DFF heating furnace at an air ratio α and an average heating rate at 200°C and above of 10 to 50°C/sec to a target heating temperature T 1 (°C) satisfying the relation below; (zone-B heating) the cold-rolled steel sheet resulting from the zone-A heating is heated in a DFF heating furnace at an air ratio ≤ 0.9 and an average heating rate at above T 1 of 5 to 30°C/sec to a target heating temperature T 2 (°C) satisfying the relation below; (zone-C heating) the cold-rolled steel sheet resulting from the zone-B heating is heated in an atmosphere containing H 2 and H 2 O, the balance being N 2 and inevitable impurities, at a log(P H2O /P H2) of not less than -3.4 and not more than -1.1 and an average heating rate at above T 2 of 0.1 to 10°C/sec to a prescribed target heating temperature T 3 (°C) of 700 to 900°C, and is held at T 3 for 10 to 500 seconds; T C ≤ − 60 Si + Mn + 775 T 1 ≥ 28.2 Si + 7.95 Mn − 86.2 α + 666 T 2 ≥ T 1 + 30 wherein [Si] and [Mn] are the contents of mass% Si and Mn present in the slab, α is not more than 1.5 and not less than 0.9, and log (P H2O /P H2) is log(H 2 O partial pressure (P H2O)/H 2 partial pressure (P H2)).