The melting curve of MgSiO(3) perovskite has been determined by means of ab initio molecular dynamics complemented by effective pair potentials, and a new phenomenological model of melting. Using first principles ground state calculations, we find that the MgSiO(3) perovskite phase transforms into post perovskite at pressures above 100 GPa, in agreement with recent theoretical and experimental studies. We find that the melting curve of MgSiO(3), being very steep at pressures below 60 GPa, rapidly flattens on increasing pressure. The experimental controversy on the melting of the MgSiO(3) perovskite at high pressures is resolved, confirming the data by Zerr and Boehler.