This study examined the axial compressive properties of glass–fiber reinforced plastic (GFRP)–confined recycled aggregate concrete–filled steel tube (RACFST) stub columns. The differences in the failure modes, load–displacement curves, and load–strain curves of the composite columns with different parameters were analyzed, including the number of GFRP layers, steel tube thickness, recycled aggregate substitution rate, and recycled aggregate concrete compressive strength. The results revealed a bulging failure mode in the middle of the GFRP–confined RACFST stub columns. With the increasing substitution rate of recycled aggregate, the bulging deformation of the specimen increased. This eventually resulted in a reduction in the stiffness and bearing capacity but an improvement in the ductility at a later stage. The early stiffness and ultimate bearing capacity of the specimen can be increased by thickening the steel tube or strengthening the recycled aggregate concrete. However, the ductility is greatly reduced in the later stage. Based on the axial compression test of GFRP–confined RACFST stub columns, the axial compression bearing capacity formula was derived. Compared with the existing formula, the formula presented in this paper has greater accuracy. In addition, a finite element (FE) model of the composite column was established to analyze the stress development during the compression process.