The paper deals with a new design concept of a hydrodynamic bearing lubricated by composite magnetic fluids, which belong to the category of liquids with a yielding shear stress if effected by a magnetic field. Development of the mathematical model of the studied bearing required to derive the equation for the pressure distribution in the thin film of lubricant exhibiting yielding shear stress, the magnitude of which depends on magnetic induction. The magnetic field in the bearing gap is controlled by the change of the current powering the electric coil, which generates magnetic flux passing through the bearing gap. The developed mathematical model was implemented in the computational procedures for transient response of rotors. The computational simulations confirm that increase in magnetic induction in the bearing gap increases the bearing load capacity and shifts the journal towards the bearing centre. The advantage of the investigated bearing is that it works on a semiactive principle. The conducted research made it possible to propose and study a new design of a controllable bearing, the operation of which is based on utilization of the change of resistance against the flow of composite ferromagnetic fluids by the action of a magnetic field.