Experimental investigation was conducted to study the pure torsional behaviour of high-strength concrete (HSC) beams strengthened with carbon-fibre-reinforced-polymers (CFRP) having minimum torsional reinforcement. A total of six beams were tested. Two beams without CFRP were assigned as control beams and the rest were strengthened using CFRP sheets. In this study, different wrap configurations, the effect of different numbers of CFRP plies, and the influence of anchors in U-wrapped test beams considered as variables were investigated. Investigation into ductility using two different concepts showed enhancement in the behaviour of strengthened beams with CFRP. The ductility of the beam strengthened with two complete CFRP layers was fifty percent higher than that of the control beams. The beam strengthened using this scheme showed a 75% increase in torsional capacity compared to the control beam, which was not strengthened. The experimental results were compared with the results from three analytical methods. The ultimate torsional strength resulting from one of the three methods, which was based upon synthesis of an analytical method and average CFRP strains obtained from experiments, was in good agreement with the experimental results.