High performance concrete has been often preferred in special engineering structures and in challenging composites products. Researchers have recently focused on the radiation shielding characteristics of these type concrete mixtures due to rising nuclear industry in the developing world. In the study, performance of reactive powder concrete was researched with regard to gamma-ray and neutron attenuation when its normal weight aggregate replaced with heavyweight aggregate (barite). For this purpose, reactive powder concrete mixtures were prepared 100% quartz aggregate, 100% barite aggregate and their blending 50–50%, by volume. Some physical and mechanical characteristics such as density, compressive strength, fracture energy, flexural strength and modulus of elasticity of the mixtures were determined. Gamma-ray attenuation coefficients and transmission thickness values were theoretically established for commonly known gamma energies (661.7, 1173.2 and 1332.5 keV). Optimization of the reactive powder mixtures was performed for both neutron and gamma-ray attenuation at 8 MeV. As a result, barite significantly increased the gamma-ray attenuation coefficients of reactive powder concrete. The mechanical performance of reactive powder concrete, however, was markedly reduced as a result of barite substitution. Replacement of quartz by barite aggregate has a more adverse impact on flexural strength than that of compressive strength. A mix that contains 40% barite aggregate of total aggregate volume was found as an optimum RPC mixture for simultaneously shielding neutrons and gamma rays.