A cooling system for a gantry of a computer tomography system which has a gantry supporting an x-ray source being positioned in a gantry housing and being rotatable around a rotation axis, the gantry housing being positioned by at least one bearing on a stationary part of the computer housing so that it can be moved relative to the housing. The cooling system comprises a cooling gas supply arrangement or device directing a cooling gas flow in the region of at least one bearing between the stationary part and the gantry housing.