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The neutron backgrounds induced by supplementary experimental materials can result in contaminations in rare event search experiments. To address this, we present the neutron background levels arising from ambient materials in the polyethylene room of the China Jinping Underground Laboratory; particularly, we compare simulated spectra with measured neutron spectra unfolded using a genetic algorithm. The genetic algorithm optimizes the continuity of the energy spectra and obtains a reasonable spectral result. A good agreement between the unfolded and simulated spectra is achieved. Moreover, estimated neutron background levels of representative ambient materials such as polyethylene, aluminum, and lead are obtained using an exposure time of 511.27 days via a 28 liter 0.5%-gadolinium-doped liquid scintillator detector. The identification of rare neutron sources can aid in background reduction in next-generation large-scale rare event experiments.