The results of the study of quartz and glauconite sand (QGS) are presented. The specific properties of QGS as a concrete aggregate are established. Due to X-ray fluorescence analysis of the QGS chemical composition it was revealed that its basic oxides are silicon, phosphorus, calcium, aluminum, iron, potassium and fluorine oxides. The scanning electron microscopy showed that glauconite in QGS is in the form of rounded grains with a size of 10–500 µm (globules), as well as earthy masses, lumpy, scale, reniform aggregates. The loose glauconite structure and its liability to absorption and cation exchange may be the reason for a higher water demand of QGS (by 20%) as compared to quartz sand (QS). It is shown that concretes with QGS differ from concretes with QS in strength by more than two times after 2, 7 and 28 days of hardening, which is probably due to a complex of factors, the amount of phosphorus oxide playing a primary role. The method of three-factor design of experiments yields the equations and response surface of the dependence of the concrete compressive and bending strength on the content of cement, sand and a hardening accelerator Master X-Seed 100 after 28 days of hardening. The obtained equations and response surfaces of the compressive and bending strength has shown that the more glauconite sand the concrete contains, the less its strength appears. Compositions with the hardening accelerator of 1.4% and QGS-QS ratio of 1:1 have the maximum strength.