The cross sections for the fission of 232Th, 235,238U, 237Np, and 239Pu target nuclei that was induced by 20- to 1000-MeV neutrons and protons were calculated. The respective calculations were based on the multiconfiguration-fission (MCFx) model, which was used to describe three basic stages of the interaction of high-energy nucleons with nuclei: direct processes (intranuclear cascade), equilibration of the emerging compound system, and the decay of the compound nucleus (statistical model). Fission barriers were calculated within the microscopic approach for isotopic chains formed by 15 to 20 nuclei of the required elements. The calculated fission cross sections were compared with available experimental data. It was shown that the input data set and the theoretical model used made it possible to predict satisfactorily cross section for nuclear fission induced by 20- to 1000-MeV nucleons.