Abstract: Using a 2.5-dimantional ideal MHD model in spherical coordinates, the catastrophe of a coronal magnetic flux rope embedded in a partly-open multipolar background magnetic field has been studied. The background field consists of a coronal streamer containing three closed bipolar fields and an open magnetic field with an equatorial current sheet. The magnetic flux rope lies below the central bipolar field, characterized by its annular and axial magnetic fluxes. There exists a critical axial flux for a given annular flux, or a critical annular flux for a given axial flux such that below each of these critical fluxes, the magnetic flux rope remains to be attached to the solar surface and the whole system stays in equilibrium. On the other hand, if the critical fluxes are exceeded, the flux rope leaves the solar surface and erupts upward, implying an existence of catastrophe for a coronal flux rope embedded in a partly-open multipolar background magnetic field. For the given example, the corresponding threshold of magnetic energy at the catastrophic point is found to be about 15% larger than the energy of the corresponding partly-open magnetic field in which the central bipolar field is fully open whereas those at the flank remain closed. The excessive energy may serve as an energy source for solar explosions such as coronal mass ejections.