A method of manufacturing a high-strength galvannealed steel sheet, having a tensile strength TS of 980 MPa or higher, wherein the tensile strength is evaluated by a tensile test performed according to JIS Z 2241 by using JIS No. 5 test piece, which was a sample taken so that the tensile direction became a perpendicular direction to the rolling direction of a steel sheet, which includes a zinc coated layer with a coating weight of 20 to 120 g/m 2 per side on a surface of a steel sheet having a chemical composition comprising, in mass%, C: 0.03 to 0.35%, Si: 0.01 to 1.00%, Mn: 3.6 to 8.0%, Al: 0.001 to 1.00%, P: 0.100% or less, and S: 0.010% or less, and optionally one or more selected from B: 0.001 to 0.005%, Nb: 0.005 to 0.050%, Ti: 0.005 to 0.100%, Cr: 0.001 to 1.000%, Mo: 0.05 to 1.00%, Cu: 0.05 to 1.00%, Ni: 0.05 to 1.00%, Sn: 0.001 to 0.200%, Sb: 0.001 to 0.200%, Ta: 0.001 to 0.100%, W: 0.001 to 0.100%, and V: 0.001 to 0.100%, with the balance being Fe and inevitable impurities, the method comprising: setting a cold rolling reduction ratio to 20% or more and 35% or less when cold rolling is performed on the steel sheet, wherein cold rolling comprises rolling by using, as a roll for final stand, a roll which has an arithmetic-average rolling roll surface roughness Ra of 3.6 μm or more, wherein the arithmetic-average rolling roll surface roughness Ra is an average surface roughness, which is set to be an average surface roughness in the roll surface C direction at 1/4, 1/2, and 3/4 positions in the roll width direction, the arithmetic-average rolling roll surface roughness Ra being measured in a contact type and being determined by measuring the surface roughness in the roll surface C direction at 1/4, 1/2, and 3/4 positions in the roll width direction at n = 3 and setting an average value of the total nine measurements as the arithmetic-average rolling roll surface roughness Ra, the measurement length being set as an average value to 2.5 mm and the cut-off being set to 0.8 mm; setting a maximum steel sheet temperature to be reached in an annealing furnace to 600°C or higher and 700°C or lower when annealing is further performed on the steel sheet, wherein the annealing comprises: setting a steel sheet transit time in a steel sheet temperature range of 500°C or higher and 700°C or lower to 30 seconds or more and 600 seconds or less; setting a hydrogen concentration in the steel sheet temperature range of 500°C or higher and 700°C or lower to 5 vol% or more and 50 vol% or less; and setting a dew point of an atmosphere in the steel sheet temperature range of 500°C or higher and 700°C or lower to - 65°C or higher and -25°C or lower; and heating the steel sheet at 450°C or higher and 600°C or lower in an alloying treatment after galvanizing treatment. setting a steel sheet transit time in a steel sheet temperature range of 500°C or higher and 700°C or lower to 30 seconds or more and 600 seconds or less; setting a hydrogen concentration in the steel sheet temperature range of 500°C or higher and 700°C or lower to 5 vol% or more and 50 vol% or less; and setting a dew point of an atmosphere in the steel sheet temperature range of 500°C or higher and 700°C or lower to - 65°C or higher and -25°C or lower; and heating the steel sheet at 450°C or higher and 600°C or lower in an alloying treatment after galvanizing treatment. <EOS>