NGC 6067 is a young open cluster hosting the largest population of evolved stars among known Milky Way clusters in the 50-150Ma age range. It thus represents the best laboratory in our Galaxy to constrain the evolutionary tracks of 5-7M_{sun}_ stars. We have used high-resolution spectra of a large sample of bright cluster members (45), combined with archival photometry, to obtain accurate parameters for the cluster as well as stellar atmospheric parameters. We derive a distance of 1.78+/-0.12 kpc, an age of 90+/-20Ma and a tidal radius of 14.8^+6.8^_-3.2_ arcmin. We estimate an initial mass above 5700M_{sun}_, for a present-day evolved population of two Cepheids, two A supergiants and 12 red giants with masses ~=6M_{sun}_. We also determine chemical abundances of Li, O, Na, Mg, Si, Ca, Ti, Ni, Rb, Y and Ba for the red clump stars. We find a supersolar metallicity, [Fe/H]=+0.19+/-0.05, and a homogeneous chemical composition, consistent with the Galactic metallicity gradient. The presence of a Li-rich red giant, star 276 with A(Li)=2.41, is also detected. An overabundance of Ba is found, supporting the enhanced s-process. The ratio of yellow to red giants is much smaller than 1, in agreement with models with moderate overshooting, but the properties of the cluster Cepheids do not seem consistent with current Padova models for supersolar metallicity.