The large-end-face roughness &sgr;1 of the tapered roller is set to be not less than 0.04 &mgr;mRa, consequently the assembling torque becomes generally constant and smaller in fluctuation over a range that the cone-back rib face roughness &sgr;2 is 0.03-0.23 &mgr;mRa. Also, the composite roughness &sgr;=(&sgr;12+&sgr;22)½ is set to be not more than 0.17 &mgr;mRa, consequently the preload retention rate on the regression curve can be made 90%. Further, the radius of curvature ratio R1/R2 resulting from dividing the convex radius of curvature R1 of the large end face of the tapered roller by the concave radius of curvature R2 of the cone-back rib face of the inner ring is set to be not more than 0.35, consequently the rotating torque becomes smaller in variation and also smaller in fluctuations over a range that the composite roughness &sgr; is 0.05-0.22 &mgr;mRa.