The dynamic performance of air foil bearings relies on a coupling between a thin air film and the frictional motion of a foil structure. A number of successful analytical techniques to predict their performance have been developed. However, the evaluation of their dynamic characteristics is still not adequate because of the mechanical complexity of the foil structure and the strong nonlinear behavior of the friction force. This work presents a nonlinear transient analysis method to predict the dynamic performance of foil bearings considering Coulomb friction. In this method, the time-dependent Reynolds equation is solved to calculate pressure distribution and a finite element method is used to simulate bump motion. The analysis is treated with a direct implicit integration technique that can handle nonlinear problems and an algorithm to solve for stick-slip motion of bump foil is applied. Using this method, the hysteretic behavior and dissipative characteristics of bump foil resulting from the unbalance excitation is observed. In addition, a number of parametric studies are performed to evaluate the effects of design parameters on the unbalance response. The parameters are friction coefficient, bump half wavelength, amount of mass unbalance, and the number of bump foil strips. The predictions of the unbalance response show that the foil bearing is very effective on the restriction of the vibration at the resonance frequency and there exist optimum values of design parameters such as friction coefficient, bump foil stiffness, and the number of bump foil strips with regard to minimizing the amplitude at the resonance frequency.