We present the results of the spectral analysis of the public data of 438 gamma ray bursts (GRBs) detected by the Fermi Gamma ray Burst Monitor (GBM) up to March 2010. For 432 bursts we could fit the time-integrated spectrum. In 318 cases we could reliably constrain the peak energy E^obs^_peak_ of their {nu}F{nu} spectrum by analyzing their time-integrated spectrum between 8keV and 35MeV. Eighty percent of these spectra are fitted by a power-law with an exponential cutoff, and the remaining with the Band function. Among these 318 GRBs, 274 belong to the long GRB class and 44 to the short.