Using the one-dimensional finite element method, the dynamic behaviour of a doubledisk rotor system with anisotropic supports is studied in this paper. First, the natural frequencies, whirl state and unbalance response of the rotor system are analysed. Then, the vibration attenuation mechanism of the rotor system under the effect of bearing damping and accelerating rotor is discussed in detail. The research results show that stiffness anisotropy makes natural frequency lines of the rotor system tend to diverge from each other. The damping in bearings not only decreases the amplitude of forward and backward whirls but also reduces the spin speed range of backward whirl. The whirl orbit of the rotor system approximates a straight line at the spin speeds near the critical point of the backward and forward whirls. For the unbalance response of the rotor system with anisotropic supports, the forward natural frequency dominates in the direction of the strong stiffness axis, while the unbalance response in the direction of the weak stiffness axis is mainly affected by the backward natural frequency. Increasing the run-up acceleration can decrease the amplitude of backward and forward whirls, but it cannot reduce the spin speed range of backward whirl.