This paper presents a finite-element analysis study of elliptical concrete columns, converted from rectangular cross sections and confined with carbon fiber-reinforced polymers (CFRP) through an enhancement/strengthening procedure, under eccentric loadings. The parameters considered for the finite-element analysis study include various eccentric loads, and the number of CFRP layers as well as their orientation with respect to circumferential axis of concrete columns. Validation of the finite-element model was performed leveraging an experimental study reported in the literature. Study findings suggest that eccentric loading versus concentric loading considerably reduces the efficiency of the CFRP wrapping. The study, however, also shows that it is possible to diminish the adverse effect of eccentric loading through proper adjustment of the wrap configuration, i.e., the number of layers as well as the orientation of the fibers.