PURPOSE: To prevent the generation of cracks in the title bearing at the time of plastic working and to prolong its service life by forming at least either of the inner ring and outer ring of a rolling bearing with the compsn. of a steel having specified contents ot C, Si, Mn, Cr, P, S and O.

CONSTITUTION: At least either of the inner ring and outer ring of a bearing is formed by subjecting a steel constituted of, by weight, 0.4 to 0.7% C, ≤0.04% Si, 0.4 to ≤1.0% Mn, 0.4 to 1.0% Cr, ≤0.025% P, ≤0.003% S, ≤0.0015% O and the balance Fe with inevitable impurities to plastic working. Then, the steel is subjected to surface hardening heat treatment if necessary. In this way, the rolling bearing having no generation of cracks even if subjected to forming working into the final shape by cold forging, etc., can be obtd. At least either of ≤0.2% Nb or V is furthermore incorporated into the above steel, by which the rolling service life can moreover be improved.