We derived atmospheric parameters and elemental abundances of Fe, O and Na for about 120 red giant stars in the Galactic globular cluster NGC 2808. Our results are based on the analysis of medium-high resolution (R=22000-24000) GIRAFFE spectra acquired with the FLAMES spectrograph at VLT-UT2 as a part of a project aimed at studying the Na-O anticorrelation as a function of physical parameters in globular clusters. We present here the anticorrelation of Na and O abundances in NGC 2808, and we discuss the distribution function of stars along this relation. Besides a bulk of O-normal stars, with composition typical of field halo stars, NGC 2808 seems to host two other groups of O-poor and super O-poor stars. In this regard, NGC 2808 is similar to M 13, the template cluster for the Na-O anticorrelation. However, at variance with M 13, most stars in NGC 2808 are O-rich. This might be related to the horizontal branch morphologies which are very different in these two clusters. The average metallicity we found for NGC 2808 is [Fe/H]=-1.10 (rms=0.065 dex, from 123 stars). We also found some evidence of a small intrinsic spread in metallicity, but more definitive conclusions are hampered by the presence of a small differential reddening.