A method of fast-neutron imaging with energy threshold is presented in this paper, which is based on an imaging plate covered with a metal foil and a hydrogen-rich foil in order to reduce the contribution from the neutrons with a lower energy such as the scattering neutrons from samples. The method is capable of effectively reducing the relative sensitivity of the imaging detector to neutrons with energies in a certain energy range. The 14 MeV neutron imaging structure with an energy threshold is designed, and it includes a TR imaging plate covered with an about 150 m Pb foil and a 500 m polyethylene foil. The calculated results show that for the present structure its sensitivity to the neutrons with smaller than 8 MeV is reduced by 30% less than that to the neutrons with 14 MeV. The fast-neutron radiography is validated experimentally on a DT neutron generator (K400). The results indicate that the neutron imaging structure with an energy threshold is available to remove the edge enhancement effect introduced by scattering neutrons from samples.