Rotors supported by gas foil bearings (GFBs) experience stability problem caused by subsynchronous vibrations. To obtain a GFB with satisfactory damping characteristics, this study presented a novel hybrid bump-metal mesh foil bearing (HB-MMFB) that consists of a bump foil and metal mesh blocks in an underlying supporting structure, which takes advantage of both bump-type foil bearings (BFBs) and MMFBs. A test rig with a nonrotating shaft was designed to estimate structure characterization. Results from the static load tests show that the proposed HB-MFBs exhibit an excellent damping level compared with the BFBs with a similar size because of the countless microslips in the metal mesh blocks. In the dynamic load tests, the HB-MFB with a metal mesh density of 36% presents a viscous damping coefficient that is approximately twice that of the test BFB. The dynamics structural coefficients of HB-MFBs, including structural stiffness, equivalent viscous damping, and structural loss factor, are all dependent on excitation frequency and motion amplitude. Moreover, they exhibit an obvious decrease with the decline in metal mesh density.