Today, the application of fiber reinforced polymer (FRP) composites has been successfully promoted for strengthening or repairing of structural members. Columns are the basic members in a structure that transfer the axial load with or without bending moment. So, strengthening these members by FRP composites and developing new methods in order to improve the efficiency of them is very important. One of the methods for strengthening the reinforced concrete (RC) columns with FRP composites is using the FRP jackets environmentally around the columns. The FRP jackets are used mainly in a condition that all or most of the fibers of composite are perpendicular to the column axis and in hoop direction to provide confinement. However, the axial compressive strength of columns can be increased by using FRP composite with longitudinal fibers; where the fiber sheets contribute by resisting compression directly. Buckling of FRP composite causes inappropriate performance of composite under compressive stresses. In longitudinally strengthened columns with FRP, buckling of FRP composite causes debonding of FRP from concrete surface. On the other hand, researches have shown that the newly developed grooving method as alternative to surface preparation can postpone or in some cases eliminate debonding of FRP sheet from the surface of the concrete beams and columns. Most of the columns in a structure are under axial-flexural loading; so, study the behavior of columns under eccentric loading seems to be necessary. In a column strengthened with longitudinal FRP composites under eccentric loading, some of the composites are under tension stresses and because of their high tension resistance, increase the strength of the columns. On the other hand, some of the composites are under compression stresses; in this case, using grooving method postpones buckling of these composites and they can play an effective role in increasing the strength of the column too. So, in this research the grooving method is used in the specimens that are strengthened with longitudinal FRP composites in order to study the effect of grooving method in postponing the buckling and debonding the FRP sheets from concrete surface and consequently increasing the strength of specimens. In addition, because of the importance of ductility in structural members such as columns, the ductility of the specimens has been investigated in this research. To perform the study, 35 cylindrical reinforced concrete specimens with 150 mm diameter and 500 mm height were tested experimentally under compression loading with eccentricity of zero, 30, 60 and 90 mm and under 4-point flexural bending. In this study, the conventional externally bonded reinforcement (EBR) and the grooving method by externally bonded reinforcement on grooves (EBROG) technique was utilized for installing the FRP sheets with longitudinal fibers. Experimental results showed that using the grooving method by EBROG technique increases the load carrying capacity of columns with longitudinal composite and by increasing the load eccentricity, the effect of longitudinal composites increased. In this case, the compression strength of specimens strengthened with longitudinal composites using EBROG technique, under zero, 30, 60 and 90 mm eccentricity of loading and under 4-point flexural bending, were respectively increased 8.3%, 12.2%, 25.8%, 36% and 53.3% compared with the unconfined specimens. Also according to the results, in all kinds of loading, grooving method is more effective in increasing the load capacity compared with EBR method. In addition, the results of studying about ductility showed that longitudinal composites were effective in increasing the ductility of the specimens. Key Words Cylindrical RC specimen, Load carrying capacity, FRP composite with longitudinal fibers, Buckling, Grooving method, Eccentric loading, 4-point flexural loading