A numerical code RFPA3D (Realistic Failure Process Analysis) is used to simulate the crack initiation and propagation in FRP-strengthened concrete beam under external loading. In our model, the FRP-strengthened concrete is assumed to be a three-phase composite composed of concrete, FRP, and interface between them. The displacement-controlled loading scheme is used to simulate the complete failure process of FRP-strengthened concrete the numerical simulation of failure process of the specimens. It is found that the main failure mode is the interfacial debonding and the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. The simulation results agree well with the experiment observations. The width of the FRP sheet is considered an important factor not only to significantly influence the debonding propagation type and crack distribution but also to control the ultimate load-capacity and ultimate strain. This study is focused on the failure process of the FRP-strengthened concrete beam and the effects of the width of FRP sheet on the failure mode and on the structural load-carrying capacity of concrete structures.