In this study, the grooving method was employed to strengthen reinforced concrete (RC) columns with longitudinal fiber-reinforced polymer (FRP) sheets, and the performance of columns was investigated under both concentric and eccentric loadings. Furthermore, the effects of longitudinal FRP sheets and the grooving method on the ductility of strengthened concrete columns were studied. For this study, 12 slender square concrete columns with a slenderness ratio of 25 were subjected to eccentric loading with various eccentricity-to-cross section ratios (e/h) equal to 0, 0.24, 0.48, and 0.72 (i.e., eccentricities of 0, 30, 60, and 90 mm). Externally bonded reinforcement (EBR) and externally bonded reinforcement on grooves (EBROG) methods were utilized for FRP strengthening of the specimens. The results demonstrated that for the eccentricity ratios of 0, 0.24, 0.48, and 0.72, the load-carrying capacity of the columns strengthened with the EBROG method increased by 10.6%, 19.6%, 68.8%, and 99.3%, respectively, compared to those of the nonstrengthened columns. Particle image velocimetry (PIV) analyses demonstrated that under all the loading conditions investigated, the grooving method effectively improved the column performance, including load-bearing and flexural capacities. Such analysis also revealed that the application of longitudinal FRP sheets led to significant enhancements in the ductility of the columns tested.