A rolled steel bar or wire rod having hot surface fatigue strength, wear resistance, and machinability even after hot forging has a composition containing C, Si, Mn, S, Cr, Mo (optional), Al, and N, with the balance being Fe and impurities. The chemical composition satisfies that fn1 defined by Formula (1) is 1.60 to 2.10. The structure of the rolled steel bar or wire rod for hot forging includes a ferrite-pearlite structure, a ferrite-pearlite-bainite structure, or a ferrite-bainite structure. A maximum value/a minimum value of average ferrite grain size, which is observed and measured randomly in 15 visual fields each having an area of 62500 μm2 in a cross section, is not more than 2.0. fn1=Cr+2×Mo (1), and each symbol of elements in Formula (1) is substituted by a content (mass %) of a corresponding element.