This paper presents the results of investigating the application of magnetorheological fluids in controlling the lateral and angular vibrations of a high-speed elevator. Numerical simulations are performed for a mathematical model with two degrees of freedom. The lateral and rotational accelerations are analyzed for different travel speeds to determine passenger comfort levels. To attenuate the elevator vibrations, the introduction of a magnetorheological damper in parallel with the passive damper of the elevator rollers is considered. To semi-actively control the dissipative forces of the magnetorheological fluids, a State-Dependent Riccati Equation (SDRE control) is proposed. The numerical results demonstrate that using an MR damper makes it possible to reduce the acceleration levels of the elevator cabin, thus improving passenger comfort and reducing the elevator’s vibration levels and wear on the mechanical and electronic components of the elevator. In addition to the results, a detailed sensitivity analysis is presented.