The band gap attenuation characteristics of finite and infinite periodic compound plate simply supported along its longitudinal edges are investigated with the wave propagation approach. Base on the boundary continuum condition between two plates, the coupled equations of finite and infinite periodic compound plate are established by transfer matrix and Bloch theorem respectively, and the relations of band gap attenuation characteristics between finite and infinite periodic compound plate are analyzed in detail. It is shown that the frequency band gap of periodic compound plate is related to exciting form and position. The frequency band gap of finite compound plate is coincident with the frequency band gap of infinite compound plate with the same mode vibration if finite compound plate is excited with one mode along its longitudinal edges. If the plate is excited with a point force, the frequency band gap is the intersection of frequency band gap of all participated modes. Besides, the influence of the structural damping on band gap is also analyzed.