In this paper, a new-type air foil bearing with combined bump foils is proposed. The bump foils are arranged and combined in the axial direction. The local and global stiffness of the bearing can be adjusted by the combination of the bump foils. Mechanical analysis of the bearing is carried out, and the mechanical model of the elastic deformation of the flat foil and the bump foils is constructed. Combined with non-isothermal Reynolds equation and energy equation, a fluid–solid coupling numerical calculation model is constructed. Through the actual bearing test research, the reliability of the established theoretical model is verified. On this basis, combined with the specific example, the influences of the structural parameters of the new-type foil bearing on its mechanical properties and lubrication performance are studied, and the specific influence curves are obtained. It is also found that the new-type bearing proposed in this paper has good adaptability to the shaft deflection. When the shaft is deflected, the bump foil at the axial end increases the minimum film height by generating large elastic deformation, which can help to avoid wear caused by direct contact between the shaft and the foil.