A strengthening technique, combining carbon fiber-reinforced polymer (CFRP) laminates and strips of wet layup CFRP sheet, is used to increase both the flexural and the energy dissipation capacities of reinforced concrete (RC) columns of square cross section of low to moderate concrete strength class, subjected to constant axial compressive load and increasing lateral cyclic loading. The laminates were applied according to the near surface mounted technique to increase the flexural resistance of the columns, while the strips of CFRP sheet were installed according to the externally bonded reinforcement technique to enhance the concrete confinement, particularly in the plastic hinge zone where they also offer resistance to the buckling and debonding of the laminates and longitudinal steel bars. The performance of this strengthening technique is assessed in undamaged RC columns and in columns that were subjected to intense damage. The influence of the concrete strength and percentage of longitudinal steel bars on the strengthening effectiveness is assessed. In the groups of RC columns of 8 MPa concrete compressive strength, this technique provided an increase of about 67% and 46% in terms of column's load carrying capacity, when applied to undamaged and damaged columns, respectively. In terms of energy dissipation capacity, the increase ranged from 40%-87% in the undamaged columns, while a significant increase of about 39% was only observed in one of the damaged columns. In the column of moderate concrete compressive strength (29 MPa), the technique was even much more effective, since, when compared to the maximum load and energy dissipation capacity of the corresponding strengthened column of 8 MPa of average compressive strength, it provided an increase of 39% and 109%, respectively, showing its appropriateness for RC columns of buildings requiring upgrading against seismic events.