This paper investigates the feasibility of strengthening of seismically deficient concrete columns with high-strength fiber composite straps. The concrete columns will be externally confined by wrapping thin glass-fiber-reinforced or carbon-fiber-reinforced straps around the column. The confinement provided by the straps will increase the stress and strain of concrete at failure and will increase its ductility. Moreover, the composite strap will prevent buckling of longitudinal bars and spalling of the shell and therefore will further increase the load carrying capacity of the column. Analytical models are developed and a seismically deficient parametric study is conducted to investigate the effectiveness of this technique for strengthening of concrete columns designed before the new seismic design provisions and codes were in place. The variables used in the parametric study include, concrete compressive strength, thickness of composite strap, clear spacing between composite straps and type of the composite strap, i.e., carbon fiber reinforced or glass fiber reinforced. The results indicate that external confinement provided by the composite straps significantly increases the strength and ductility of concrete columns.