Externally-bonded (EB) fibre reinforced polymer (FRP) retrofitting system has emerged as a promising strengthening technique to improve flexural performance of concrete structures. This paper presents the results of an experimental program studying the behaviour of concavely-curved soffit reinforced concrete (RC) strengthened in flexure with EB carbon fibre reinforced polymer (CFRP) composites. Thirty-two RC beams were statically tested in this program. Of these beams, twenty-three were curved soffit beams with varying degree of curvature ranging between 5 mm/m and 20 mm/m, and nine beams were constructed with flat soffit as control beams. The ultimate capacity, failure mode, flexural stiffness, and the ductility of these beams are analysed and discussed. Based on the experimental results, concavely-curved soffit RC beams with the smallest degree of curvature strengthened with EB-CFRP performed better than beams with higher degree of curvature strengthened with similar CFRP system. This study identifies gaps of knowledge in existing design guidelines and codes and presents recommendations for designers on EB-CFRP technology.