The neutron-induced fission cross section of 245Cm was measured at n_TOF in a wide energy range and with high resolution. The energy dependence, measured in a single measurement from 30 meV to 1 MeV neutron energy, has been determined with 5% accuracy relative to the 235U(n,f) cross section. In order to reduce the uncertainty on the absolute value, the data have been normalized at thermal energy to recent measurements performed at ILL and BR1. In the energy range of overlap, the results are in fair agreement with some previous measurements and confirm, on average, the evaluated cross section in the ENDF/B-VII.0 database, although sizable differences are observed for some important resonances below 20 eV. A similar behavior is observed relative to JENDL/AC-2008, a reactor-oriented database for actinides. The new results contribute to the overall improvement of the databases needed for the design of advanced reactor systems and may lead to refinements of fission models for the actinides.