Abstract Metal-based polymer composites, a new category of advanced materials, are advantageous for effective protection of radiation field. Recent report of fabrication of tungsten (W)-Poly methyl methacrylate (PMMA) composite microcellular foams with enhanced mechanical strength properties opens up the possibility of its use in radiation attenuation. Objective of this theoretical study is to assess the efficacy of W-based polymer composite, a new lead-free shielding material for attenuating coupled neutron-gamma radiations. Current paper utilizes open-source Monte Carlo code FLUKA to evaluate shielding efficiency of PMMA composites reinforced with varying concentration W particles. Study shows that, adding even 20 vol% of W particles can significantly improve radiation shielding ability of PMMA. Performance of analogous composition Pb-based polymer composite is also examined to demonstrate its inadequacy in radiation protection compared to W-based composite. Study reveals an interesting fact that for any shield dimension, total radiation dose follows an initial descending trend with increase in heavy metal (W/Pb) proportion up to certain optimum value where dose becomes minimum, beyond that dose increases. Optimum heavy metal concentrations are found to be 70 vol% and 30 vol% for W and Pb respectively, with minimum dose for Pb shield being two orders of higher magnitude. Study is further extended to investigate shielding efficiency of conventional double-layer laminates employing W and PMMA in both high-Z/low-Z and low-Z/high-Z configurations as well as optimum concentration of W-PMMA composite and PMMA. It is shown that among all the potential designs, newly introduced composite-based double-layer shield performs best in terms of volumetric dose while single-layer optimized composite shield offers least specific dose.