A high-strength cold-rolled steel sheet which has an excellent ductility and a stretch-flangeability, the steel sheet consisting of, by mass percentage: 0.05 to 0.4% of C; 0.1 to 2.5% of Si; 1.0 to 3.5% of Mn; 0.001 to 0.03% of P; 0.0001 to 0.01% of S; 0.001 to 2.5% of Al; 0.0001 to 0.01% of N; 0.0001 to 0.008% of O; and optionally one or more of 0.005 to 0.09% of Ti; 0.005 to 0.09% of Nb; 0.0001 to 0.01% of B; 0.01 to 2.0% of Cr; 0.01 to 2.0% of Ni; 0.01 to 2.0% of Cu; 0.01 to 0.8% of Mo; 0.005 to 0.09% of V; one or more of Ca, Ce, Mg, and REM at 0.0001 to 0.5% by mass percentage in total, and a remainder composed of iron and inevitable impurities, wherein a steel sheet structure contains by volume fraction 10 to 45% of a ferrite phase, 10 to 50% of a tempered martensite phase, and a remaining hard phase, wherein when a plurality of measurement regions with diameters of 1 μm or less are set in a range from 1/8 to 3/8 of a thickness of the steel sheet, hardness measurement values in the plurality of measurement regions are arranged in ascending order for hardness distribution purposes, an integer N0.02 which is a number obtained by multiplying a total number of the hardness measurement values by 0.02 and, if present, by rounding up a decimal number, is achieved, a hardness of a measurement value which is an N0.02-th largest value from a smallest hardness measurement value is regarded as a 2% hardness, an integer N0.98 which is a number obtained by multiplying the total number of the hardness measurement values by 0.98 and, if present, by rounding down the decimal number is obtained, and a hardness of a measurement value which is an N0.98-th largest value from the smallest hardness measurement value is regarded as a 98% hardness, the 98% hardness is 1.5 or more times as high as the 2% hardness, wherein a kurtosis K* of the hardness distribution between the 2% hardness and the 98% hardness is equal to or more than -1.2 and equal to or less than -0.4, wherein an average crystal grain size in the steel sheet structure is 10μm or less, wherein the remaining hard phase includes 10 to 60% of one of or both a bainitic ferrite phase and a bainite phase and 10% or less of a fresh martensite phase by volume fractions, and wherein a difference between a maximum value and a minimum value of Mn concentration in a base iron in a thickness range from 1/8 to 3/8 of the steel sheet is equal to or more than 0.4% and equal to or less than 3.5% when converted into the mass percentage. 0.05 to 0.4% of C; 0.1 to 2.5% of Si; 1.0 to 3.5% of Mn; 0.001 to 0.03% of P; 0.0001 to 0.01% of S; 0.001 to 2.5% of Al; 0.0001 to 0.01% of N; 0.0001 to 0.008% of O; and optionally one or more of 0.005 to 0.09% of Ti; 0.005 to 0.09% of Nb; 0.0001 to 0.01% of B; 0.01 to 2.0% of Cr; 0.01 to 2.0% of Ni; 0.01 to 2.0% of Cu; 0.01 to 0.8% of Mo; 0.005 to 0.09% of V; one or more of Ca, Ce, Mg, and REM at 0.0001 to 0.5% by mass percentage in total, and a remainder composed of iron and inevitable impurities, wherein a steel sheet structure contains by volume fraction 10 to 45% of a ferrite phase, 10 to 50% of a tempered martensite phase, and a remaining hard phase, wherein when a plurality of measurement regions with diameters of 1 μm or less are set in a range from 1/8 to 3/8 of a thickness of the steel sheet, hardness measurement values in the plurality of measurement regions are arranged in ascending order for hardness distribution purposes, an integer N0.02 which is a number obtained by multiplying a total number of the hardness measurement values by 0.02 and, if present, by rounding up a decimal number, is achieved, a hardness of a measurement value which is an N0.02-th largest value from a smallest hardness measurement value is regarded as a 2% hardness, an integer N0.98 which is a number obtained by multiplying the total number of the hardness measurement values by 0.98 and, if present, by rounding down the decimal number is obtained, and a hardness of a measurement value which is an N0.98-th largest value from the smallest hardness measurement value is regarded as a 98% hardness, the 98% hardness is 1.5 or more times as high as the 2% hardness, wherein a kurtosis K* of the hardness distribution between the 2% hardness and the 98% hardness is equal to or more than -1.2 and equal to or less than -0.4, wherein an average crystal grain size in the steel sheet structure is 10μm or less, wherein the remaining hard phase includes 10 to 60% of one of or both a bainitic ferrite phase and a bainite phase and 10% or less of a fresh martensite phase by volume fractions, and wherein a difference between a maximum value and a minimum value of Mn concentration in a base iron in a thickness range from 1/8 to 3/8 of the steel sheet is equal to or more than 0.4% and equal to or less than 3.5% when converted into the mass percentage.