A geometrically nonlinear finite element analysis of flexural edge waves for the composite jet engine fan blade model is presented. For the transient response problem of the composite fan blade subjected to local impact loading with foreign objects, existence of flexural edge wave in the region of the leading edge and the trailing edge was confirmed for the first time in computer simulation. Amplitudes of edge wave decrease exponentially with distance from the edge. These waves have dispersive characteristic even at low frequencies and are important in the region of the leading edge and the trailing edge of composite blade structures. It was found that delaminations of the leading edge in experimental results for ATP (Advanced TurboProp) blade model presented in the literature were related to this edge wave propagation along the free boundary.And also it was clear that just after the impact, higher order flexural waves are generated owing to local deformations. These higher order waves possess dispersive property related to impact position,impactor's velocity,contact area with foreign objects,contact time etc. The higher order wave is one of the dominant factors on complicate impact fracture mechanism of composite structures. A computational simulation using finite element method is very efficient to study the mode of the edge wave generation and propagation and to predict fan blade impact damage.