Gas foil bearing has been used in high-speed turbomachinery for its high speed, high adaptability, and eco-friendly. The stability of the rotor bearing system is greatly enhanced due to the flexible foil support structure. In the foil supporting structure, vibration energy of the rotor bearing system can be absorbed by the Coulomb friction dissipation. In order to evaluate the frictional dissipation on bearing performance, a quasi-2-dimensional mechanical model is proposed considering the Coulomb friction. The Coulomb damping dissipation characteristics of the bearing in operating conditions are analyzed by coupling gas film. Frictional analysis is conducted on the bump foil bearing with different structural parameters, such as bump height, foil thickness, friction coefficient and number of bump foil strips. The stiffness of the foil bump is less affected by the base load. In the process of foil bearing design, the optimal friction coefficient, bump height should be properly selected in favor of either foil bearing stiffness or damping characteristics. In addition, the overall performance of bump foil bearing is strongly affected by the number of bump foil strips.