It has been well known that concrete structures exposed to acid and sulfate environments such as sewer, sewage and wastewater, soil, groundwater, and seawater etc. show significant decrease in their durability due to chemical attack. Such deleterious acid and sulfate attacks lead to expansion and cracking in concrete, and thus, eventually result in damage to concrete matrix by forming expansive hydration products due to the reaction between portland cement hydration products and acid and sulfate ions. Objectives of this experimental research are to investigate the effect of mineral admixtures on the resistance to acid and sulfate attack in concrete and to suggest high-resistance concrete mix against acid and sulfate attack. For this purpose, concretes specimens with three types of cement (ordinary portland cement (OPC), binary blended cement (BBC), and ternary blended cement (TBC) composed of different types and proportions of admixtures) were prepared at water-biner ratios of 32% and 43%. The concrete specimens were immersed in fresh water, 5% sulfuric acid, 10% sodium sulfate, and 10% magnesium sulfate solutions for 28, 56, 91, 182, and 365 days, respectively. To evaluate the resistance to acid and sulfate for concrete specimens, visual appearance changes were observed and compressive strength ratios and mass change ratios were measured. It was observed from the test results that the resistance against sulfuric acid and sodium sulfate solutions of the concretes containing mineral admixtures were much better than that of OPC concrete, but in the case of magnesium sulfate solution the concretes containing mineral admixtures was less resistant than OPC concrete due to formation of magnesium silicate hydrate (M-S-H) which is non-cementitious.