The existence of either eccentricity or slenderness has a significant effect on the mechanical properties of a structure or member. These properties can change the working mechanism, failure mode, and bearing capacity of the structure or member. A concrete-filled, glass fibre-reinforced, polymer tube composite column has the same problem. We carried out experiments on the influences of eccentricity and slenderness on the mechanical properties of concrete-filled, glass fibre-reinforced, polymer tube composite columns. The experimentally recorded stress–strain relationships are presented graphically, and the ultimate axial stresses and strains and the FRP tube hoop strains at rupture were tabulated. The results indicate that the influences of slenderness and eccentricity on the composite columns were significant with regard to the axial strain, hoop strain, ultimate bearing capacity, lateral displacement, and failure mode. Based on the existing research literature and the results reported in this paper, the bearing capacity formula of a composite slender column under an eccentric load was established. The theoretical results were in good agreement with the experimental results.