This study presents an investigation of the mix proportion and mechanical properties of one-part alkali-activated geopolymer concrete (GPC). The procedure for determining the mix proportion of one-part alkali-activated GPC, which uses a solid alkali activator in crystal form, is proposed. The proposed procedure was applied to a series of mixed proportions of GPC with different amounts of solid crystalline alkali activator (AA), water (W), and superplasticizer (SP), using the ratio between them to the total amount of binder (B, fly ash, and granulated blast furnace slag) by weight in order to evaluate their effect on the workability and compressive strength of the GPC. The slump, compressive and tensile strength, and elastic modulus of the one-part alkali-activated GPC were tested in various ways. The test results showed that solid crystalline alkali activators, water, and superplasticizers have significant effects on both the workability and compressive strength of GPC. The amount of one-part alkali activator should not exceed 12.0% of the total binder amount by weight (AA/B = 0.12) in order not to lose the workability of GPC. The minimum W–B ratio should be at least 0.43 to ensure the workability of the sample when no superplasticizer is added. An amount of 2.5% can be considered as the upper bound when using superplasticizer-based polysilicate for GPC. In addition, the elastic modulus and various types of tensile strength values of the one-part alkali-activated GPC were evaluated and compared with that predicted from compressive strength using equations given by two common ACI and Eurocode2 codes for ordinary Portland cement (OPC) concrete. Modifications of the equations showing the relationships between splitting tensile strength and compressive strength, as well as between elastic modulus and compressive strength and the development of compressive strength under the time provided by ACI and Eurocode2 for OPC concrete, were also made for one-part alkali-activated GPC.