A bearing according to the present invention includes a cylindrical member formed on and around an outer member of a usual bearing. To firmly connect the cylindrical member to the outer member, grooves having an inclination relative to the axial direction of the bearing are formed so that the grooves do not cross one another on the outer surface of the outer member. The cylindrical member is made of a resin material by molding, and the resin, which is melted by heat in the molding process, enters into and adheres to the grooves. In this manner, the cylindrical member is firmly connected to the outer member so that movement in both of the rotational and axial directions of the bearing is prevented. The grooves formed on the outer surface of the outer member may be grouped, and their inclination relative to the axial direction may be alternately reversed group by group.