This paper utilized granulated blast furnace slag (GBFS), fly ash (FA), and zeolite powder (ZP) as the binders of ternary geopolymer concrete (TGC) activated with sodium silicate solution. The effects of alkali content (AC) and alkaline activator modulus (AAM) on the compressive strength, flexural tensile strength and elastic modulus of TGC were tested and the SEM micrographs were investigated. The experimental results were then compared with the predictions based on models of mechanical properties, and the amended models of TGC were proposed taking account of the effects of AC and AAM. The results indicated that increasing AC and reducing AAM which were in the specific ranges (5% to 7% and 1.1 to 1.5, respectively) had positive effects on the mechanical properties of TGC. In addition, the flexural tensile strength of TGC was 27.7% higher than that of OPC at the same compressive strength, while the elastic modulus of TGC was 25.8% lower than that of OPC. Appropriate prediction models with the R² of 0.945 and 0.987 for predicting flexural tensile strength and elastic modulus using compressive strength, respectively, were proposed. Fitting models, considering the effects of AC and AAM, were also proposed to predict the mechanical properties of TGC.