A tapered roller bearing is designed to have a roller loading ratio in the range of 0.7 to 0.92 and a ratio of roller length to roller diameter in the range of 1.1 to 1.7 whereby oil agitation loss and rolling viscous resistance are reduced for achieving the reduction of running torque. Crownings are provided which are designed to have an outer-ring crowning parameter (=RCO/LRO) in the range of 30 to 150 and an inner-ring crowning parameter (=RCI/LRI) in the range of 50 to 260, provided that RCO denotes the radius of an outer ring crowning, LRO denotes the raceway length of an outer ring, RCI denotes the radius of an inner ring crowning and LRI denotes the raceway length of an inner ring. Thus, the rolling viscous resistance is reduced for achieving the reduction of running torque.