Abstract: The semi active decentralized control of nonlinear structures with uncertain parameters is studied. Firstly, the degenerated Bouc-Wen hysteretic model is utilized to simulate the restoring forces, and the error state equation of a sub-control system is established by considering the uncertainty of the model parameters (mass, stiffness and damping) and the coupling between subsystems. Secondly, a sub-controller is designed which composes of a guaranteed cost control term and an adaptive approximation control term. The guaranteed cost control term is obtained by solving the guaranteed cost control problem which is transformed into a linear matrix inequality. The approximation control term is determined by the adaptive control law of RBF neural network, and its stability and boundedness of the weights are proved by Lyapunov stability theory. And then a guaranteed cost adaptive RBF neural network robust decentralized control (GCARBF) algorithm for nonlinear vibration control of uncertain structures is established. A nonlinear 8-story building is selected as a numerical example to evaluate the control performances of the proposed algorithm. The MR semi active decentralized control design and the simulation analysis of 0.3 g~0.8 g intensity are carried out. Numerical simulation results indicate the effectiveness and superiority of the proposed algorithm.