The equations of motion and boundary conditions governing the vibration of nonsymmetric composite plates with active and passive dampings layer are derived. The analytical solution is first obtained for frequencies and loss factors of the plates with active constrained layer damping treatments. The distributions of electric potential across, the thickness of piezoelectric, layer and relevant governing equations are obtained when the direct and inverse, piezolectric effects are considered. The influence of the direct and inverse piezoelectric effects on the frequencies and loss factors are investigated.