This paper presents a calculation procedure for evaluating the properties of limestone–calcined clay–cement (LC3) concrete, an emerging construction material. First, a kinetic hydration model of the composite is proposed, which can analyze the individual reaction degrees of cement, calcined clay, and limestone powder in hardening LC3 blends. The dilution effect and chemical reactions of the mineral admixtures and the nucleation effect of limestone powder are characterized. The reaction coefficients of the ternary composite hydration model do not change as the mixture composition of concrete changes. The masses of calcium hydroxide (CH) and combined water and the hydration heat are calculated using the reaction degrees of binder components. The strength development is predicted using a linear equation of the reaction degrees of the binder components. Second, the contents of carbonatable hydration products and porosity are determined using the hydration model. Furthermore, the depth and degree of carbonation are calculated on the basis of material components and exposure conditions. The results of the analysis for calcium hydroxide, combined water, heat, strength, and degree of carbonation are consistent with experimental results. In summary, the proposed calculation procedure is valuable for analyzing the hydration, chemical, heat, strength, and carbonation properties of LC3 concrete with various mixture compositions.