The PN-EN 197-1:2012 standard allows the use of additives as the main component above 5.0% by mass, as well as as a secondary component in an amount less than 5.0% by mass of cement. Proper selection of additives positively affects the rheological characteristics and hardened concrete parameters during longer maturity periods. Additives have already become an integral component of concrete mixes. The aim of the research is to confirm the possibility of using the tested additive in the composition of concrete mixes in an amount of 15% relative to the amount of cement, which would solve the problem of storing and utilizing waste generated during the production of broken chalcedonite aggregates. The planned laboratory tests were carried out for concrete of three classes, C30/37, C35/45, C40/50, according to the PN-EN 206+A1:2016-2 standard, with the addition of chalcedonite dust in a constant amount of 15% relative to cement, and three series without additives as control series. The additive used for concrete mixes was chalcedonite dust with a diameter below 72 µm. It is waste from a broken aggregate mine. The research program included rheological tests of fresh concrete mix, i.e., air content, consistency, bulk density, as well as parameters of hardened concrete mix-compressive strength, absorbability, and capillary uptake. Compressive strength was tested after 7, 14, 28, 56, and 90 days. The laboratory tests aimed to verify whether the addition of 15% chalcedonite dust additive would not worsen the predicted hardened concrete parameters resulting from the designed concrete classes. All three tested series, C30/37, C35/45, and C40/50, with the addition of 15% chalcedonite dust relative to the amount of cement, achieved the assumed strength classes after 28 days of maturation. Concrete mix components were correctly designed. The addition of chalcedonite dust to the concrete mix did not cause a decrease in compressive strength to the extent that the analyzed series did not meet the normative requirements for concrete classes according to the PN-EN 206+A1:2014 standard. The results of absorbability testing indicate water absorption below 5%, while the increase in sample mass in the capillary uptake test gained similar values.