Composite materials have attracted wide attention in strengthening of structural members. In this study, the behavior of rectangular reinforced concrete (RC) strengthened with fiber reinforced polymer (FRP) laminates under pure torsion was investigated numerically and validated by existing data from literature. Various practical strengthening configurations were considered and the efficiency of them was illustrated. Concrete damage plasticity constitutive model was used and required parameters was drawn. Good agreement in terms of torque-twist behaviors of RC beams strengthened with FRP laminates before and after cracking was found. Reasonable steel and FRP reinforcement responses as well as crack patterns were achieved and the failure modes of all the specimens were modeled correctly. A parametric study was carried out and parameter such as number of FRP plies, concrete compressive strength, and FRP strip orientations were considered. The results showed that the torsional capacity could improves by increasing the number of FRP plies and concrete compressive strength. Moreover, no significant change in the torsional capacity of RC beams when it was strengthened with a 45 or with a 90 FRP laminate was observed.