© 2016 ACM.In this study, vibrations of a rotor-bearing system supported by tilted air bearing are numerically investigated. Air flow between rotor and bearing surfaces is modelled using Reynold's equation with an introduced new clearance function for tilted air bearing. In order to calculate air film forces, Reynold's equation is solved using Differential Transform and Finite Difference hybrid numerical solution method. Dynamic motions of the rotor-bearing system supported by air bearings are modelled with air film forces in four degrees-of-freedom. In order to investigate effects of the bearing tilt on the vibrations of the rotor, one of the air bearing is modelled with a certain amount of tilt angle and the model is simulated for different rotor angular speeds.