High-energy secondary neutrons, produced by the interaction of galactic cosmic rays with the atmosphere, spacecraft structure and planetary surfaces, contribute to a significant fraction to the dose equivalent in crew members and passengers during commercial aviation travel, and astronauts in space missions. The Los Alamos Nuclear Science Center (LANSCE) neutron facility's ICE House 30L beamline is known to generate neutrons that simulate the secondary neutron spectra of earth's atmosphere. The neutron spectrum is also similar to that measured onboard spacecraft like the MIR and International Space Station (ISS). To evaluate the biological damage, we exposed human fibroblasts in vitro to the LANSCE neutron beams without degrader at an entrance dose rate of 25 mGy/h and analyzed the micronuclei (MN) induction. The cells were also placed behind a 9.9 cm water column to study the effect of shielding in the protection of neutron induced damages. It was found that the dose response in the MN frequency was linear for the samples with and without shielding and the slope of the MN yield behind the shielding was reduced by a factor of 3.5. Compared to the MN induction in human fibroblasts exposed to a γ source at a similar low dose rate, the RBE was found to be 16.7 and 10.0 for the neutrons without and with the 9.9 cm water shielding, respectively.