It is known that the effect of fluid upon structural vibration is very large with the estimation of vibrational performance on floating structures, therefore fluid-structure coupled analysis method which combine the added mass matrix into FEM has been used. Thence pretty accurate eigenvalue of structural vibration can be estimated for many cases of ship structure. But the vibration level can not be estimated so well, because the damping of structure and fluid viscosity is not known. Therefore it is necessary for the estimation of vibration level to investigate the damping caused by fluid viscosity. In this paper, a new theory of added damping matrix based on dissipation energy caused by fluid viscosity is described. The distribution of flow velocity in the vibrational boundary layer is determined by assuming laminar flow in spite of existence of turbulence, then shearing stress is decided using virtual kinematic viscosity coefficient. Dissipation energy caused by fluid viscosity is formulated as the function of the nodal amplitude of the BEM mesh model. The added damping matrix can be obtained by comparing that with dissipation energy of usual damping matrix of FEM. The difference of dissipation energy between in deep water and in shallow water is clarified by using the added damping matrix. A new idea of reduced added damping matrix is defined, then combination analysis of the experimental modal analysis and BEM is executed using the reduced added mass & damping matrix. The validity of the added damping matrix is verified by comparing with some experiments in the deep water and the shallow water.