FRP (fiber-reinforced polymer)–concrete–steel double-skin square tubular (FCSST) columns are composed of an outside FRP tube, an inside steel tube and the concrete filled between them. Under the continuous constraint of the outside and inside tube, the strain, strength and ductility of concrete are improved significantly compared with those of traditionally reinforced concrete without lateral restraint. Additionally, the outside and inside tube not only function as the permanent formwork in casting but improve the bending and shear resistance of composite columns. Meanwhile, the hollow core also reduces the weight of the structure. Through the compressive testing of 19 FCSST columns subjected to eccentric load, this study focuses on the influence of eccentricity and layers of axial FRP cloth (away from the loading point) on the evolution of axial strain along the cross-section, axial bearing capacity, axial load–lateral deflection curve and other eccentric properties. The results can provide basis and reference for the design and construction of FCSST columns and are of great theoretical significance and practical value for the application of composite columns in the engineering of structures in a corrosive environment and other harsh conditions.