Based on the Hamilton's principle, a dynamic model of high-storey building damping structure with a mass pendulum considering the rigid-elastic coupling effects is discussed. In the model, the high-storey building was regarded as an upright cantilever beam namely infinite degrees of freedom. And the model had two variables, which were lateral displacement of the beam and angle of rotation of the mass pendulum. Then, a nonlinear rigid-elastic coupling equation was formed considering the constraint condition of geometric nonlinearity. Finally ,The finite dimensions dynamic equations considering the rigid-elastic coupling effects were obtained by taking advantage of Galerkin method, and the validity of the theories presented in this paper was verified by a numerical simulation example.