Aims. The Karin cluster is a small asteroid family that formed 5.8±0.2 Myr ago in the outer main belt. This is an exceptionally young age for an asteroid family. To investigate the composition and homogeneity of the members of this family, we started a spectroscopic survey in the visible and in the near-IR. Methods. We observed 24 Karin asteroid members in the visible and 6 members in the near-IR. Results. In the visible range, all the objects share the same characteristics: a maximum around λ = 0.75 μm, and a spectral slope spanning a continuous but limited range; in the NIR, our spectra show a similar behaviour. Our results suggest global homogeneity of the parent body and none of the investigated objects seems to be an interloper. These results are consistent with the dynamical hypothesis of a common origin. Finally, the range of spectral slopes is similar with the range of slopes for OC meteorites.We interpret this result as an indication of a low degree of spatial alteration for the observed surfaces. This result is coherent with the young age of the family.