Based on the Monte Carlo particle transport program MCNP, a novel glass fiber/B4C/epoxy resin composite for neutron shielding with high strength and low density was developed. Its neutron transmissivity was calculated under the Am-Be neutron source condition to study the difference of neutron shielding performance between the glass fiber/B4C/epoxy resin composite and traditional shielding materials. Furthermore, effects of B4C mass fraction of the composite on the shielding performance for neutrons with different energy(slow neutron, intermediate neutron, fast neutron) were analyzed. The results show the composites with 10% B4C mass contents have more advantages on the neutron shielding performance , especially the slow neutron shielding performance in comparison with polyethylene/boron containing composites and Al-B4C alloy. With the further increasing of the B4C contents, no remarkable increase is observed. Monte Carlo method is demonstrated feasible in optimization design of neutron shielding materials and the results provide a theoretical basis for design and preparation of a new neutron shielding composite.