Prestressing tendons made of fiber-reinforced polymers (FRP) are a promising alternative to conventional steel tendons in prestressed concrete structures owing to their corrosion resistance.However, the shear strength of FRP prestressed concrete beams is still not well understood. This paper presents a theoretical model for predicting the shear strength of prestressed concrete beams with FRP tendons or strands, with and without FRP shear reinforcement. The model is an extension of the Compression Chord Capacity Model (CCCM), originally proposed for steelreinforced concrete structures, which has been adapted to account for the particularities of FRP as active and passive reinforcement. The model is applicable to rectangular, T and I sections, and accounts for reductions in shear strength caused by bond loss in FRP tendons. An experimental validation of the model has been performed by comparing the theoretical predictions for 55 shear tests found in the literature. Good accuracy has been obtained, not only in predicting the ultimate shear capacity of beams but also in identifying shear-bond failures observed in some tests.