The neutron-induced fission cross section of 237Np was measured between 3 eV and 2 MeV by the time-of-flight technique using a gas scintillator as a fission fragment detector. Two measurements were carried out with the Saclay 60-MeV Linac used as a pulsed-neutron source. The first measurement, with a nominal resolution of 2 ns/m, was performed in the 3-eV to 35-keV energy range, where the fission cross section exhibits the well-known intermediate structure. The samples were cooled to liquid nitrogen temperature to reduce the Doppler broadening predominant below 50 eV. Thanks to good statistics and to a very low background, a shape resonance analysis was possible up to 155 eV, the quoted uncertainties on the fission widths being essentially due to inaccurate neutron widths. The second experiment was run from 25 keV to 2 MeV, with a nominal resolution of 0.3 ns/m, and showed a structureless fission cross section. The agreement with the Physics 8 underground nuclear explosion data seems to be very poor in the resonance region, whereas it is more satisfactory for higher energies. Neptunium-238 fission barrier parameters were deduced from the collected data and agree fairly well with published results.