The neutron fission cross section of 241Am was measured in the energy range from 10 to 1030 keV using 235U as a standard. The measurements were carried out at the Karlsruhe 3-MV pulsed Van de Graaff accelerator with 7Li targets for the generation of a continuous neutron spectrum below 140 keV and monoenergetic neutron spectra between 120 and 1030 keV. Fission events were detected by measuring the prompt fission neutrons with an NE-213 liquid scintillator with pulse-shape discrimination. The flight path was as short as 60 mm in measurements with continuous neutron spectra leading to a moderate energy resolution. The statistical uncertainty was between 0.8 and 10% and the systematic uncertainty between 5.4 and 8.5%. Discrepancies were found when comparing our results with those of other experiments.