Due to the environmental impacts resulting from the production of Ordinary Portland cement (OPC), the drive to develop alternative binders that can totally replace OPC is gaining huge consideration in the construction field. In the current study, attempt was made to determine the strength characteristics of glass fibre-reinforced fly ash based geopolymer concrete. Sodium hydroxide (NaOH) and sodium silicate (Na2SiO3) were used as alkaline solutions (for activation of geopolymer reaction) at 12, 16, 20 M. Glass fibres were added to the geopolymer concrete in varying proportions of 0.1–0.5% (in steps of 0.1%) by weight of concrete. A constant weight ratio of alkaline solution to fly ash content of 0.43 was adopted for all mixes. British standard concrete test specimens were cast for measuring compressive strength, split-tensile strength, and flexural strength. Concrete specimens were cured by heating in oven at 90 °C for 24 h and natural environment, respectively. From the results, thermally cured concrete samples had better mechanical properties than the ambient (natural) cured samples. Thermally cured concrete specimen, containing 0.3% glass fibre and 16 M NaoH, achieved a maximum compressive strength of 24.8 MPa after 28 d, while naturally cured samples achieved a strength of 22.2 MPa. There was substantial increase in tensile strength of geopolymer concrete due to the addition of glass fibres. Split tensile strength increased by 5–10% in glass fibre-reinforced geopolymer concrete, containing 0.1–0.5% glass fibre and 16 M NaoH when compared to the unreinforced geopolymer concrete (1.15 MPa)