Fiber-reinforced polymer (FRP) textile reinforced engineered cementitious composite (ECC) matrix (TRE for short) is a newly developed composite system with great potential for the strengthening and life extension of damaged reinforced concrete (RC) columns after fire exposure. It combines the advantages of the lightweight and high strength of FRP textile and the ultra-high ductility of ECC material. However, there is a lack of research on the use of the TRE system to strengthen fire-damaged RC columns. This paper presents an experimental study on the axial compressive behavior of fire-damaged square RC columns strengthened with the TRE system. A total of 13 specimens were prepared and tested under axial compression. The test variables included the fire-exposure time (2 h or 3 h) used to produce the initial pre-damage of RC columns, the type of cementitious matrix (ECC or mortar), the number of TRE layers (2 layers or 3 layers), and the thickness of the concrete cover (20 mm or 40 mm). The failure modes, load capacity, secant stiffness, ultimate displacement, load–displacement curves of the specimens and the hoop tensile strains in the outermost layer of the CFRP textiles were investigated and discussed. The typical failure mode of the strengthened specimens was characterized by tensile rupture of the fiber rovings bridging the main crack in the strengthening jacket. The results showed that the use of the TRE system could significantly increase the load capacity, secant stiffness and ultimate displacement of fire-damaged RC columns. Depending on the design parameters, the enhancement percentages in the load capacity varied between 18% and 126%.