This paper describes the results of numerical simulation performed to investigate the torsional behavior of reinforced concrete (RC) beams strengthened with externally bonded fiber reinforced cementitious matrix (FRCM) composite. A nonlinear finite element analysis was performed using LS-DYNA. FE predictions were in reasonable agreement with experimental results of FRCM-strengthened beams under torsional loading in terms of failure mode, torsional strength, and corresponding twist per unit length. A parametric study was also carried out to study the influence of concrete compressive strength and FRCM composite strip width and spacing. Results showed that the torsional strength increases with increasing concrete compressive strength when failure is governed by crushing of the concrete strut. When failure is governed by fiber rupture, the torsional strength was not sensitive to concrete compressive strength. The parametric study also showed that the torsional strength increases with increasing fiber reinforcement ratio, although the increase in torsional strength is not directly proportional to the increase in fiber reinforcement ratio.