The fission cross sections of 235U for neutrons having energies between 0.2 and 8.2 MeV have been measured with neutrons from the 7Li(p, n) reaction. The neutron energy scale was calibrated by the 7Li(p, n) and 10B(p, n) neutron thresholds, and the flux was measured with a black neutron detector. The fission cross sections, averaged over the 252Cf fission neutron spectrum, were determined as 1.202 b, with an uncertainty of 2 to 3%.