A rolling bearing to exhibit outstanding initial (cage) acoustic characteristics at the start of operation under a low temperature atmosphere, suppress fretting damages (abrasions) and reduce bearing torque by making the radius of curvature of the cross-sectional shape of the inner raceway and the radius of curvature of the cross-sectional shape of the outer raceway equal to 51.0% to smaller than 60.0% of the diameter of the rolling element, and packing a grease composition comprising a base oil that is a mixture of a lubricant containing a polar group in its molecular structure and a non-polar lubricant and a metallic soap-based thickener containing a long-fiber material with a major axis part length of at least 3 .mu.m.