We propose and demonstrate experimentally super-collimation of light beams by an axisymmetric diffractive metamirror-an axisymmetric concentric dielectric ring structure positioned in front of a mirror at a distance of several micrometers. By super-collimation, we mean the formation of a well-collimated beam characterized by a substantial enhancement of its axial component in the far-field domain. In the reported experiments, the axial intensity of the field was enhanced by around six times. Such axisymmetric super-collimators could be especially useful for improving the emission spatial quality of micro-lasers, when integrated as one (or both) resonator mirrors.