The influence of a specified damage on transient propagation of Lamb wave in a composite laminated plate is studied by finite element analysis. The finite element formulation is developed for the laminated plate with embedded or surface-bonded piezoelectric layers. A higher order laminate model is used to describe the displacement field of both composite laminate and piezoelectric layer. The damaged area is modeled by a localized loss of stiffness and quantified by a degradation coefficient κ. Piezoelectric materials act as both actuators and sensors for generating and receiving Lamb waves. Numerical results show that the waveform, wave peaks and the arrival time of the transmitted Lamb wave are distinctly correlated with quantified degradation coefficient κ of the damaged area, which are helpful to damage detection for a composite laminated plate in a new way.