A comprehensive study of the present work aimed to investigate the radiation shielding features for W–Cu composites materials with high density. Isostatic hot pressing technique was applied to obtain W85 wt%Cu15 wt% and W75 wt%Cu25 wt% composites with various thickness (0.6, 0.9, 1.2, 1.5 and 2.7 cm). Composites were the pollycristalline samples with well packed microstructure. The statistical grain size distribution performed that the size of an agrolemerated copper grains increases with the Cu content rising. X-ray diffraction (XRD) analysis showed that the main spectrum lines of the composites are corresponded to the bcc phase of tungsten and fcc phase of copper. The linear attenuation coefficient (LAC) was detected experimentally using a NaI detector at various incoming photon energy. The highest values of LAC are found 2.11 and 4.33 cm−1 for W75 wt%Cu25 wt% and W85 wt%Cu15 wt%, respectively, at low energy 0.266 MeV while the lowest values (0.44 and 0.48 cm−1 for W75 wt%Cu25 wt% and W85 wt%Cu15 wt%, respectively) are observed at high energy 1.25 MeV. From the obtained results, it can deduce the discussed W–Cu composites are suitable to be used in several applications of radiation protection.