method for manufacturing a high-strength galvanized steel sheet comprising the steps of: performing hot rolling and cold rolling of a steel slab having the following chemical composition, on a percent by mass basis, more than 0.015% to less than 0.10% of C, 0.5% or less of Si, 1.0% to 1.9% of Mn, 0.015% to 0.050% of P, 0.03% or less of S, 0.01% to 0.5% of sol. Al, 0.005% or less of N, less than 0.30% of Cr, 0.005% or less of B, less than 0.15% of Mo, 0.4% or less of V, less than 0.020% of Ti, optionally at least one of less than 0.02% of Nb, 0.15% or less of W, 0.1% or less of Zr, 0.5% or less of Cu, 0.5% or less of Ni, 0.01% or less of Ca, 0.01% or less of Ce, 0.01% or less of La, 0.01% or less of Mg, 0.2% or less of Sn and 0.2% or less of Sb, and the balance being iron and inevitable impurities, in which 2.2 ≤ Mneq ≤ 3.1, % Mn + 3.3 % Mo ≤ 1.9, and ([%Mn]+3.3[%Mo])/(1.3[%Cr]+8[%P]+150B*)<3.5 are satisfied, where Mneq = % Mn + 1.3 % Cr + 8 % P + 150 B * + 2 % V + 3.3 % Mo, B * = % B + % Ti / 48 × 10.8 × 0.9 + % Al / 27 × 10.8 × 0.025, [%Mn], [%Cr], [%P], [%B], [%Ti], [%AI], [%V], and [%Mo] represent the contents of Mn, Cr, P, B, Ti, sol. Al, V, and Mo, respectively, [%B]=0 is represented by B*=0, and B*≥0.0022 is represented by B*=0.0022; then in a continuous galvanizing line, performing heating in a range of 680°C to 750°C at an average heating rate of less than 5.0°C/sec; subsequently performing annealing at an annealing temperature in a range of 750°C to 830°C; performing cooling so as to set an average cooling rate from the annealing temperature to immersion in a galvanizing bath to 2°C to 30°C/sec and so as to set a holding time in a temperature region of 480°C or less during the cooling to 30 seconds or less; then performing galvanizing by the immersion in the galvanizing bath; and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the galvanizing, or further performing an alloying treatment after the galvanizing, and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the alloying treatment. performing hot rolling and cold rolling of a steel slab having the following chemical composition, on a percent by mass basis, more than 0.015% to less than 0.10% of C, 0.5% or less of Si, 1.0% to 1.9% of Mn, 0.015% to 0.050% of P, 0.03% or less of S, 0.01% to 0.5% of sol. Al, 0.005% or less of N, less than 0.30% of Cr, 0.005% or less of B, less than 0.15% of Mo, 0.4% or less of V, less than 0.020% of Ti, optionally at least one of less than 0.02% of Nb, 0.15% or less of W, 0.1% or less of Zr, 0.5% or less of Cu, 0.5% or less of Ni, 0.01% or less of Ca, 0.01% or less of Ce, 0.01% or less of La, 0.01% or less of Mg, 0.2% or less of Sn and 0.2% or less of Sb, and the balance being iron and inevitable impurities, in which 2.2 ≤ Mneq ≤ 3.1, % Mn + 3.3 % Mo ≤ 1.9, and ([%Mn]+3.3[%Mo])/(1.3[%Cr]+8[%P]+150B*)<3.5 are satisfied, where Mneq = % Mn + 1.3 % Cr + 8 % P + 150 B * + 2 % V + 3.3 % Mo, B * = % B + % Ti / 48 × 10.8 × 0.9 + % Al / 27 × 10.8 × 0.025, [%Mn], [%Cr], [%P], [%B], [%Ti], [%AI], [%V], and [%Mo] represent the contents of Mn, Cr, P, B, Ti, sol. Al, V, and Mo, respectively, [%B]=0 is represented by B*=0, and B*≥0.0022 is represented by B*=0.0022; then in a continuous galvanizing line, performing heating in a range of 680°C to 750°C at an average heating rate of less than 5.0°C/sec; subsequently performing annealing at an annealing temperature in a range of 750°C to 830°C; performing cooling so as to set an average cooling rate from the annealing temperature to immersion in a galvanizing bath to 2°C to 30°C/sec and so as to set a holding time in a temperature region of 480°C or less during the cooling to 30 seconds or less; then performing galvanizing by the immersion in the galvanizing bath; and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the galvanizing, or further performing an alloying treatment after the galvanizing, and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the alloying treatment. [%Mn], [%Cr], [%P], [%B], [%Ti], [%AI], [%V], and [%Mo] represent the contents of Mn, Cr, P, B, Ti, sol. Al, V, and Mo, respectively, [%B]=0 is represented by B*=0, and B*≥0.0022 is represented by B*=0.0022; then in a continuous galvanizing line, performing heating in a range of 680°C to 750°C at an average heating rate of less than 5.0°C/sec; subsequently performing annealing at an annealing temperature in a range of 750°C to 830°C; performing cooling so as to set an average cooling rate from the annealing temperature to immersion in a galvanizing bath to 2°C to 30°C/sec and so as to set a holding time in a temperature region of 480°C or less during the cooling to 30 seconds or less; then performing galvanizing by the immersion in the galvanizing bath; and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the galvanizing, or further performing an alloying treatment after the galvanizing, and performing cooling to 300°C or less at an average cooling rate of 5°C to 100°C/sec after the alloying treatment.