•TPB test was performed to explore the effect of basalt fiber on geopolymer concrete.•The strengthening mechanisms of basalt fiber were explored by SEM.•A decrease in crack length of basalt fiber–reinforced FAGCs was observed via DIC.•MTH method was used to analyze elastic properties of basalt fiber–reinforced FAGCs. A comprehensive experimental study was conducted to explore the fracture characteristics of basalt fiber–reinforced fly ash geopolymer concretes (FAGCs) with different fiber contents (0.025%, 0.05%, 0.1%, 0.15%). The fracture behaviors of the basalt fiber–reinforced FAGCs, such as load-crack mouth opening displacement curve, fracture toughness, fracture energy, crack propagation length, were investigated by three-point bending tests, and their strengthening mechanisms were explored by scanning electron microscopy. In addition, the Mori–Tanaka homogenization (MTH) method was introduced to analyze the elastic properties of the basalt fiber–reinforced FAGCs. It was found that the addition of basalt fibers improved the peak load, fracture toughness, and fracture energy of the basalt fiber–reinforced FAGCs, and the most significant improvements were noticed in the concrete with the basalt fiber content of 0.05%. Moreover, a decrease in the crack length of the basalt fiber–reinforced FAGCs was observed before the load level of the post-80% peak load. The elastic properties of the basalt fiber–reinforced FAGCs were analyzed based on the MTH theory, and numerical results were found to be in good agreement with experimental findings.