In order to obtain the damping properties of the co-cured composite structures with double-layer damping membranes embedded， the natural frequency and loss factor of the structure are calculated by Rayleigh-Ritz method based on the first-order shear deformation theroy. The calculation results are compared with the finite element method， and the correctness of the theory is verified. The law of the natural frequency and loss factor variation with the change the damping layer position and shear modulus is obtained. The results show that the natural frequency of the structure decreases firstly and then increases with the increase of the mid-plane distance between the two damping layers， and there is a minimum value. When the mid-plane distance between the two damping layers increases， the loss factor increases firstly and then decreases， and there is an optimal value for the design. The natural frequency of the structure increases monotonously with increasing structural shear modulus； as the shear modulus increases， the loss factor of the structure no longer monotonically changes.