Dark Matter (DM) as a weakly interacting massive particle could annihilate or decay and give rise to high energy gamma-rays. Then an indirect search for Dark Matter is possible by means of the Large Area Telescope on board the Fermi satellite. A relatively large signal is expected from the regions where the Dark Matter is expected to have the greatest density, such as the central region of the Milky Way. This region also hosts many high-energy gamma ray sources, of many different classes. Furthermore diffuse gamma-ray emission due to cosmic-ray interactions with interstellar gas and radiation is detected from the same direction. A greatly improved understanding of the gamma ray emission from the Galactic Center region is going to be obtained with the Fermi LAT first-year data. The data along with refined modelling of the diffuse emission and a careful evaluation of the discrete sources will improve our ability to disentangle a potential dark matter signal from the astrophysical background and to place new limits on the mass and annihilation rate (or lifetime) of Dark Matter particle
