Rolled H-shaped steel, having a chemical composition comprising: in mass%, C: 0.01 to 0.25%; Si: 0.05% to 0.50%; Mn: 0.40 to 2.50%; P: 0.050% or less; S: 0.050% or less; N: 0.020% or less; Cu: 0.70% or less; Ni: 0.70% or less; Cr: 0.50% or less; V: 0.12% or less; Mo: 0.30% or less; Nb: 0.08% or less; Ti: 0.05% or less; Al: 0.07% or less; REM: 0.010% or less; Ca: 0.0050% or less; and the balance: Fe and inevitable impurities, wherein: a top 5% average value of Mn concentrations in a most embrittled portion in a flange is 1.6 times or less an Mn concentration at a position of 1/6 in a flange width direction from an end face in the flange width direction and 1/4 in a flange thickness direction from a face of a flange positioned on a side opposite to that of a web; and a top 5% average value of Mn concentrations in a central segregation portion dispersed in a region 15 mm or more apart from a center of the flange width toward one end face or both end faces in the flange width direction and within 2 mm from a flange surface layer in the thickness direction is not less than 1.1 times nor more than 1.6 times the Mn concentration at the position of 1/6 in the flange width direction from the end face in the flange width direction and 1/4 in the flange thickness direction from the face of the flange positioned on the side opposite to that of the web, wherein the Mn concentration is measured according to the description. in mass%, C: 0.01 to 0.25%; Si: 0.05% to 0.50%; Mn: 0.40 to 2.50%; P: 0.050% or less; S: 0.050% or less; N: 0.020% or less; Cu: 0.70% or less; Ni: 0.70% or less; Cr: 0.50% or less; V: 0.12% or less; Mo: 0.30% or less; Nb: 0.08% or less; Ti: 0.05% or less; Al: 0.07% or less; REM: 0.010% or less; Ca: 0.0050% or less; and the balance: Fe and inevitable impurities, wherein: a top 5% average value of Mn concentrations in a most embrittled portion in a flange is 1.6 times or less an Mn concentration at a position of 1/6 in a flange width direction from an end face in the flange width direction and 1/4 in a flange thickness direction from a face of a flange positioned on a side opposite to that of a web; and a top 5% average value of Mn concentrations in a central segregation portion dispersed in a region 15 mm or more apart from a center of the flange width toward one end face or both end faces in the flange width direction and within 2 mm from a flange surface layer in the thickness direction is not less than 1.1 times nor more than 1.6 times the Mn concentration at the position of 1/6 in the flange width direction from the end face in the flange width direction and 1/4 in the flange thickness direction from the face of the flange positioned on the side opposite to that of the web, wherein the Mn concentration is measured according to the description. a top 5% average value of Mn concentrations in a most embrittled portion in a flange is 1.6 times or less an Mn concentration at a position of 1/6 in a flange width direction from an end face in the flange width direction and 1/4 in a flange thickness direction from a face of a flange positioned on a side opposite to that of a web; and a top 5% average value of Mn concentrations in a central segregation portion dispersed in a region 15 mm or more apart from a center of the flange width toward one end face or both end faces in the flange width direction and within 2 mm from a flange surface layer in the thickness direction is not less than 1.1 times nor more than 1.6 times the Mn concentration at the position of 1/6 in the flange width direction from the end face in the flange width direction and 1/4 in the flange thickness direction from the face of the flange positioned on the side opposite to that of the web, wherein the Mn concentration is measured according to the description.