A shielding benchmark experiment has been performed to obtain the spectra of neutrons penetrating 10- to 100-cm-thick iron shields and 25- to 200-cm-thick concrete shields and to investigate the accuracy of various calculation codes using a 137-MeV quasi-monoenergetic neutron source. The source neutrons are produced from a 1.0-cm-thick lithium target bombarded with 140-MeV protons, and the energy spectra are measured with the time-of-flight (TOF) method using a NE213 organic liquid scintillator. The neutrons emitted in the forward direction were collimated with a 150-cm-thick iron collimator with 10- × 12-cm aperture. TOF and unfolding methods are applied to obtain the energy spectra behind the shield for the peak energy region and continuous-energy region, respectively. Monte Carlo calculations with PHITS and MCNPX are compared with the measured data. The comparison shows that the calculated spectra are in good agreement with the measured spectra.