To provide an improved rolling bearing assembly having an improved resistance to electric corrosion, which can provide a proper performance and can be assembled at a reduced cost, the rolling bearing assembly includes an inner race (1), an outer race (2) and a circumferential of rolling elements (3) rollingly interposed between the inner and outer races (1) and (2). An electrically insulating layer (4) is formed on a surface of one of the inner and outer races (1) and (2), which is held in contact with a housing or a shaft when the rolling bearing assembly is mounted. This electrically insulating layer (4) is made of a gray alumina containing Al.sub.2O.sub.3 mixed with TiO.sub.2 in a quantity chosen to be equal to or smaller than 1 wt % relative to the total weight of the gray alumina.