A bearing is a mechanical component that transmits rotation and supports load. Depending on the type of rotating mechanism, bearings are categorized into ball bearings and tapered-roller bearings. Tapered-roller bearings are superior to ball bearings in load-bearing capabilities. They are used in applications where high loads, such as, the wheel bearings for commercial vehicles and trucks, aircraft, high-speed trains, and heavy-duty spindles for heavy machinery must be supported. The demand for reducing the friction torque in automobiles has recently increased owing to carbon-emission regulations and fuel-efficiency requirements. Therefore, research on the friction torque of bearings is essential; studies have been conducted on lubrication, friction, and contact in tapered-roller bearings. There have also been studies on lip friction, roller misalignment, and so on; however, research on the influence of roller geometries and material properties is scarce. This study investigated the friction torque of tapered-roller bearings taking roller geometries and material uncertainties into consideration. The friction torque of tapered-roller bearings subject to axial loads was calculated theoretically and compared to experimental results. A Monte Carlo simulation was performed to evaluate the influence of roller geometries and material uncertainties on the friction torque of the bearings. The results of the Monte Carlo simulation showed a distribution skewed to the left. A correlation analysis of the random variables suggested that the outer raceway half angle and rib angle had a significant impact on the friction torque. In conclusion, the method proposed in this study enables the identification of factors influencing the torque of tapered-roller bearings. It is anticipated that these results can be utilized in the design of tapered-roller bearings.