This study investigates the behavior and failure modes of FRP confined concrete wrapped with different FRP schemes, including fully wrapped, partially wrapped and non-uniformly wrapped concrete cylinders. By using the same amount of FRP, this study proposes a new wrapping scheme that provides a higher compressive strength and strain for FRP-confined concrete, in comparison with conventional fully wrapping schemes. A total of thirty three specimens were cast and tested, with three of these specimens acting as reference specimens and the remaining specimens wrapped with different types of FRP (CFRP and GFRP) by different wrapping schemes. For specimens that belong to the descending branch type, the partially wrapped specimens had a lower compressive strength but a higher axial strain as compared to the corresponding fully wrapped specimens. In addition, the non-uniformly wrapped specimens achieved both a higher compressive strength and axial strain in comparison with the fully wrapped specimens. Furthermore, the partially wrapping scheme changes the failure modes of the specimens and the angle of the failure surface. A new equation that can be used to predict the axial strain of concrete cylinders wrapped partially with FRP is proposed.