We report the results of XMM-Newton observations of Sgr A*, the radiative counterpart of the massive black hole at the nucleus of our Galaxy, performed in the frame of the guaranteed time survey program of the Galactic Center region. The discovery of bright X-ray flares from Sgr A* with Chandra in October 2000 have opened new perspectives to understand the processes at work in this object and in general in black holes accreting at low accretion rates. We report here the important results obtained with XMM-Newton on the Sgr A* high-energy flaring activity and we discuss the implications on the models and the future observational perspectives.