Fission and capture reactions were simultaneously measured in the neutron-induced reactions of Am-241 at the spallation neutron facility of the Japan Proton Accelerator Research Complex (J-PARC). Data for the neutron energy range of E-n=0.1-20 eV were taken with the TOF method. The fission events were observed by detecting prompt neutrons accompanied by fission using liquid organic scintillators. The capture reaction was measured by detecting gamma rays emitted in the deexcitation of the compound nuclei using the same detectors, where the prompt fission neutrons and capture gamma rays were separated by a pulse shape analysis. The cross sections were obtained by normalizing the relative yields at the first resonance to evaluations or other experimental data. The ratio of the fission to capture cross sections at each resonance is compared with those from an evaluated nuclear data library and other experimental data. Some differences were found between the present values and the library/literature values at several resonances.