An aerodynamic bearing for mounting a shaft for a turbo compressor having two annular axial bearing disks and a hollow cylindrical radial bearing bush. The two axial bearing disks are spaced apart and form a cavity between them for receiving a shaft sleeve connected to the shaft, and the two axial bearing disks each have an axial bearing surface facing the cavity for forming an axial gas cushion in an axial bearing gap between the axial bearing surface and the shaft sleeve. The radial bearing bush has a radial bearing surface radially inward for forming a radial gas cushion in a radial bearing gap between the radial bearing surface and the shaft for the radial mounting of the shaft, and the radial bearing bush is formed integrally and/or materially with one of the axial bearing disks as a combination bearing bush.