A shielding benchmark experiment has been performed to obtain the experimental data of neutrons penetrated through iron and concrete shields by using 140-, 250-, and 350-MeV p-Li quasi-monoenergetic neutrons. The quasi-monoenergetic neutrons were emitted from a 1-cm-thick Li target bombarded with 140-, 250-, and 350-MeV protons. The neutrons emitted in the forward direction were extracted into the time-of-flight room through a collimator of 12- × 10-cm aperture embedded in a 150-cm-thick concrete wall. The concrete and iron shield blocks were set at the exit of the collimator. Neutron energy spectra behind the shields were measured by a multimoderator spectrometer (3He proportional counter covered with polyethylene moderator of various thicknesses). Neutron energy spectra behind concrete and iron shields with different thicknesses were obtained down to thermal energy. The experimental results were compared with calculation results by the Monte Carlo simulation code PHITS. These experimental results will be useful as benchmark data to investigate the accuracy of various transport calculation codes.