Many existing concrete structures suffer from low quality of concrete and inadequate confinement reinforcement. These deficiencies cause low strength and ductility. Wrapping concrete by carbon fiber reinforced polymer (CFRP) composite sheets enhances compressive strength and deformability. In this study, the effects of the thickness of the CFRP composite wraps on the behavior of concrete are investigated experimentally. Both monotonic and repeated compressive loads are considered during the tests, which are carried out on strengthened undamaged specimens, as well as the specimens, which were tested and damaged priorly and strengthened after repairing. The experimental data shows that, external confinement of concrete by CFRP composite sheets improves both compressive strength and deformability of concrete significantly as a function of the thickness of the CFRP composite wraps around concrete. Empirical equations are also proposed for compressive strength and ultimate axial deformation of FRP composite wrapped concrete. Test results available in the literature, as well as the experimental results presented in this paper, are compared with the analytical results predicted by the proposed equations.