The aim of this study was to investigate the properties of fiber-reinforced pervious concrete. Ordinary cement, silica fume, coarse aggregate, and basalt fibers were used to produce the concrete mix. The fibers were mixed with pervious concrete at the levels of 0 kg/m3, 2 kg/m3, 4 kg/m3, 6 kg/m3, and 8 kg/m3 to the investigate their influence on the mechanical and physical properties of pervious concrete. It could be observed that the cubic compressive strength, axial compressive strength, and flexural strength increased and then decreased as the content of basalt fiber increased, while the permeability and porosity of the pervious concrete decreased with the increase in the basalt fiber content. The mesostructure of pervious concrete was also studied through industrial computed tomography (ICT); the testing phenomenon showed that the fibers had a significant influence on the arrangement of the aggregate, cement paste, and the interfacial transition zone, and excessive basalt fiber resulted in poor characteristics of the interfacial transition zone (ITZ) and inferior strength properties. It was found that incorporating a basalt fiber content of 4 kg/m3 could achieve a balance between the mechanical and physical properties of pervious concrete, which was suitable for structural applications.