Application of Fiber Reinforcement Polymer (FRP) for strengthening or retrofitting structural members has been widely developed in recent years. Among different structural members, strengthening of concrete columns is of great significance due to the important role of undergoing concentric or eccentric loads as their collapse leads to great damages in the whole building. Today, columns bearing concentric or eccentric loads could be designed in smaller cross sections in comparison to the past with the application of high strength materials and advanced molding methods. This would result in the construction of slender columns. Strengthening of concrete columns could be achieved by the use of FRP sheets with fibers parallel to the longitudinal axis of the column. One of the reasons for inappropriate performance of FRP composites under compressive stress is the buckling of their fibers. In columns strengthened with FRP sheets, the buckling of the FRP sheets would result to debond. On the other hand, development and investigations on a new grooving method have shown a great potential to postpone the debonding of FRP sheets of the concrete substrate in concrete beams and columns. As most of the structural columns experience eccentric loadings, study the behavior of slender column under eccentric loading is inevitable. If longitudinal sheets are used to strengthening columns, some parts of them will be under amplified tensile stress and due to their high tensile strength, the bearing capacity of the column would increase. Moreover, the other parts of the FRP sheet would be under compressive stress and because of the used grooving method their buckling would be postponed. So by undergoing the compressive stress, the composites have an effective role in loading increment. In this study, grooving method for strengthening concrete columns with longitudinal FRP sheet was employed in order to investigate the performance of column under concentric and eccentric loadings. Furthermore, regarding the importance of ductility and bending stiffness of the columns, the effect of strengthening concrete columns with longitudinal FRP sheets by means of grooving method on the ductility and stiffness was studied. For this reason, 12 slender square concrete columns with the sectional size of 125 mm and height of 900 mm (slenderness ratio of 25) under eccentric loading with different eccentricities of 0, 30, 60, and 90 mm were tested. In construction of the columns the two common methods of surface preparation including Externally Bonded Reinforcement (EBR) and grooving method, were employed. The results showed that in the slender columns strengthened with longitudinal FRP sheets using the grooving method, the load carrying capacity enhancements of 10.6, 19.6, 68.8, and 99.3 percent relative to those of the references were achieved for 0, 30, 60, and 90 mm eccentricities, respectively. Additionally, in all loading cases, the grooving method improved the bearing capacity more significantly than the EBR method. According to the ductility and bending stiffness analysis, the application of longitudinal FRP sheets significantly increases the ductility and bending stiffness of the columns. Key Words Slender Square Reinforced Concrete Column, Longitudinal FRP Composites, Externally Bonded Reinforcement (EBR), Grooving Method (GM), Loading with Eccentricity, Particle Image Velocimetry (PIV).