The strengthening and retrofitting technique with fiber-reinforced polymer (FRP) composites on reinforced concrete (RC) columns has been widely popular. Compared with concentric compression behaviors of rectangular FRP-confined concrete columns, there are only limited investigations on their eccentric behaviors. Additionally, the applicability of existing design codes obtained from tested small-size columns in calculating load capacity of large-size columns has not been reasonably explained. In view of this, this paper developed a meso-scale numerical analysis method using a random aggregate model based on consideration of concrete heterogeneity. A series of rectangular carbon FRP (CFRP)-confined RC columns having different cross-sectional heights were modelled to investigate the influences of corner radius and size effect on their eccentric compression behaviors. Simulated results showed that there was a transformation of failure mode from brittle compression failure to ductile tensile failure with the increasing load eccentricity. An identical globally failure mode for rectangular columns having different cross-sectional heights was observed whereas crack widths became larger obviously with the increasing cross-sectional height. Regarding the axial load versus mid-height deflection relationship, the corner radius had a significant influence on maximum axial load and softening stage, especially at smaller load eccentricities. One can see that from nominal interaction diagrams, small-eccentrically-loaded columns exhibited more obvious size effect than large-eccentrically-loaded columns. The safety factor of load capacity decreased with the increasing cross-sectional height compared with existing design codes of ACI 440.2R-17 and GB 50608, illustrating that design codes appear to be not conservative for large-size specimens. Taking the influence of size effect into account, the design equations suggested by ACI 440.2R-17 were modified in this study, and the rationality of this correction methodology was verified against simulated data and results of tested large-size rectangular columns.