In this paper, an equation for the calculation of the frictional torque of a dry-lubricated tapered roller bearing (TRB) is provided in which the effect of the roller skewing is emphasized. Calculations were performed to investigate the effect of the roller skewing on the torque of dry-lubricated TRB for two representative preload methods, that is, axial force preload and axial displacement preload. The results show that a proper roller skewing angle under axial force preload benefits the reduction of the TRB torque. However, the roller skewing angle should not exceed a certain critical value; otherwise, it will cause a steep rise in the TRB torque. Finally, the critical value of the roller skewing angle as a function of the friction coefficient and cage pocket clearance is presented. The developed torque model provides a tool for the internal design and torque optimization of dry-lubricated TRBs.