Today, with the development of nuclear technology and radiation therapy equipment, radiation protection is important. This study aimed to design heavy concrete with high compressive strength and effective protection against neutron and gamma rays. In this study, 11 types of concrete with different mixing designs including 88 samples were made. In these samples, iron ore aggregates galena, limonite, hematite, polypropylene fibers, nanoparticles, micro-particles of silicon, and B4C powder have been used. Concrete quality coefficient, compressive strength, gamma, and neutron attenuation coefficients were measured for all samples. Also, the neutron attenuation coefficient for all samples was calculated using the Monte Carlo simulation (MCNPX) code and compared with the experimental values. The density, neutron attenuation coefficient, and compressive strength of concrete samples varied from 2.37 to 3.17 g/cm3, from 0.0162 to 0.0306 cm2/g, and from 48.0 to 81.3 MPa respectively. The linear gamma attenuation coefficient and gamma-ray tenth value layer (TVL) were obtained from 0.148 to 0.398 cm-1 and 15.74 to 5.85 cm respectively. These results showed that the highest neutron and gamma attenuation coefficients were obtained for concrete containing 70% galena iron ore and 20% boron carbide and the highest compressive strength belonged to sample G15 containing 15% galena iron ore and 1.8% boron carbide. G70 was the best concrete regarding the quality factor, defined as the product of multiplying the compressive strength and linear attenuation coefficients of neutron and gamma.