Neutron-induced fission cross-sections of minor actinides have been measured using the n_TOF white neutron source at CERN. Geneva, as part of a large experimental program aiming at collecting new data relevant for nuclear astrophysics and for the design of advanced reactor systems. The measurements at n_TOF take advantage of the innovative features of the n_TOF facility, namely the wide energy range, high instantaneous neutron flux and good energy resolution. Final results on the fission cross-section of (233)U, (245)cm and (243)Am from thermal to 20 MeV are here reported, together with preliminary results for (241)Am. The measurement have been performed with a dedicated Fast Ionization Chamber (FIC), a fission fragment detector with a very high efficiency, relative to the very well known cross-section of (235)U, measured simultaneously with the same detector.