PURPOSE: To uniform stress distribution of a contact part and to further improve bearing rolling longevity by extending the bearing central side of a crowning at the contact part of a roller and inner and outer rings against the bearing end part side.

CONSTITUTION: A full crowning C1 is provided on a rolling surface 3c1 of a tapered roller 3c, but a center Y2 of the crowning C1 is offset by a size S to the side of a large end surface 3c3 from a center Y1 of the roller 3c. Consequently, a region C12 at the side of a small end surface 3c2 of the crowning C1 becomes larger than a region C13 on the side of the large end surface 3c3. The region C12 is drawn in a spherical surface of a radius r2 with a point 02 as its center, and the region 13 is drawn in a spherical surface of a radius r1 with a point 01 as its center. The region C12 and the region C13 smoothly continue to each other, and the region 12 continues to small end surface roundness R2 and the region C13 to large end surface roundness R3 respectively and smoothly. Accordingly, a skew to prevent normal rolling of the tapered roller 3c is hardly caused.