Neutron energy spectra behind concrete and iron shields were measured for quasi-monoenergetic neutrons above 200 MeV using a Bonner sphere spectrometer (BSS). Quasi-monoenergetic neutrons were produced by the 7Li(p,xn) reaction with 246-MeV and 389-MeV protons. Shielding materials are concrete blocks with thicknesses from 25 cm to 300 cm and iron blocks with thicknesses from 10 cm to 100 cm. The response function of BSS was also measured at neutron energies from 100 MeV to 387 MeV. In data analysis, the measured response function was used and the pingpong scattering effect between the BSS and the shielding material was considered. The neutron energy spectra behind the concrete and iron shields were obtained by the unfolding method using the MAXED code. Ambient dose equivalents were obtained as a function of a shield thickness successfully.