This article presents the results of research that dealt with the development of non-traditional concrete using a hybrid alkali-activated cement. It is concrete based on by-products from a metallurgical plant that replaced 100% of the natural aggregates. Steel slag (CSS, fraction: 0/8 mm) was used as a filler in combination with air-cooled slag (ACBFS, fraction: 8/16 mm and 16/32 mm). Portland blended cement (CEM II/B-S 42.5N) and H-CEMENT were used as binding components in the development of the concrete mixture designs. Both of these cements were produced by Považská cementáreň, a.s., Ladce. Attention was focused on testing the physical and mechanical properties of the developed concretes in various environments. An aqueous environment was selected as the first environment for the placement of test specimens (cubes with 150 mm edges and prisms with dimensions of 100 × 100 × 400 mm3) according to the ČSN EN 206-1 standard and the outdoor environment (August to October). The determination of the cube strength was made after 7, 28, and 90 days, the determination of the flexural and compressive strength was made at the end of the prisms, and the determination of the dynamic modulus of elasticity was made after 28 days on the prisms. The test results of the test specimens, which were placed in two environments, were compared and it was found that, after 90 days, the outdoor environment caused a decrease in the concrete’s strength characteristics when using Portland blended cement (CEM II/ B-S 42.5N) of about 8%; in contrast, when using H-CEMENT, the concrete’s strength increased by about 14%. The use of H-CEMENT and the addition of PUZZOLANIT in the amount of 30% in combination with CEM II/B-S 42.5N in the amount of 70% reduced the decrease in the strength of the concrete after 90 days by about 3%. The research results confirm the suitability of using H-CEMENT and the addition of PUZZOLANIT for the production of concrete based on steel slag (CSS) and air-cooled slag (ACBFS).