The enhancement of the mechanical properties of recycled aggregate concrete (RAC) has long piqued the interest of researchers. Based on a brief review of the existing methods for improving the mechanical properties of RAC, this paper proposed a new composite column—steel fiber-reinforced recycled concrete-filled GFRP tube (SF-RACFFT) column. To investigate the axial compressive performance of concrete-filled GFRP tube (CFFT) columns, 36 specimens were designed and fabricated. The variables considered included the mass replacement rate of recycled coarse aggregate (MRCA: 0, 50%, and 100%), steel fiber volume content (VSF: 0, 0.6%, 1.2%, and 1.8%), and GFRP tube thickness (T: 4 mm, 6 mm, and 8 mm). The failure patterns of these CFFT columns were compared, the contribution of the GFRP tube to the axial bearing capacity was quantified, and the axial stress–strain responses were analyzed. Results showed that as the GFRP tube thickness increased, the peak axial stress of the CFFT columns increased by 20.8%∼54.2%. Replacing natural coarse aggregate (NCA) with 100% recycled coarse aggregate (RCA) resulted in a reduction of 8.6%∼12.4% in peak stress; while adding an appropriate amount of steel fibers could improve the peak stress. Finally, based on the evaluation of existing models, a strength enhancement model and a strain enhancement model for SF-RACFFT columns were proposed.