A surface of a tapered roller (3) is bombarded with truly spherical fine silica particles having a diameter of 100 [mu]m or less to form recesses and protrusions, and then bombarded with abrasive particles to remove the protrusions. The abrasive particles comprise rubber particles having a diameter of 1 mm and, bonded to the surface thereof in an amount of 5 mass%, abrasive diamond grains having an average diameter of 10 [mu]m. Thus, a plurality of recesses each having a circular opening with a diameter of 50 [mu]m or less are formed in the surface of the tapered roller (3) at a distance therebetween of 200 [mu]m or less. These recesses serve as moderate oil pits to heighten the ability to form an oil film on the surface of the roller. The torque of the tapered-roller bearing can hence be reduced.