The dynamic problem of constrained layer damping (CLD) plate was investigated with the transfer function method in this paper. The equations of motion and the boundary conditions were derived by using the Hamilton principle. Then the unknown displacements were expressed in Fourier series. With the introduction of the state vector, the governing equation in state space was established by the distributed parameter transfer function method. The closed-form solutions of natural frequencies, loss factors and curves of frequency response of a simply supported CLD plate were obtained. Numerical predictions of this paper agreed very well with the results of NASTRAN.