In order to obtain the general formulation of coposite-particle scattering in the three-body Faddeev formalism, Weinberg's separation of the T-matrix into a part including a composite-particle pole and a remaining part is applied to the two-body T-matrix in the Faddeev equation. By this procedure, the Faddeev equation is reduced into coupled integral equations, where one of their kernels is just the solution of the generalized Lovelace equation coming from the pole parts in the two-body T-matrices. From these coupled integral equations, a generalized composite-particle scattering amplitude can be obtained, in which the amplitude is defined by using the off-shell form factor and is the analytic extension of the amplitude defined by the residues at the poles corresponding to the composite particles. It is noticeable that, in this formulation, bound state and resonance are treated in the unified way.