In order to fully describe the dynamic behavior of the magnetic levitation ball system which has nonlinear, open-loop instable and rapid response characteristics, RBF-ARX model with linear functional weights (LFWRBF-ARX model) was established. Different from a general RBF-ARX model, the LFWRBF-ARX model introduces a local linear structure as the weights of output layer. This model varies with the working-point, it is a locally linear ARX model when the working-point is fixed and it becomes a globally nonlinear ARX model when the working-point changes. According to the model structure, a structured nonlinear parameter optimization method (SNPOM) was applied to identify the structure, linear and nonlinear parameters of model. Then the identified model-based predictive controller was designed. The results show that the LFWRBF-ARX model may capture the local and global dynamic characteristics of the magnetic levitation ball system well, and the ball may be controlled to levitate stably. The control results are better than those of the general ARX model and RBF-ARX model-based control.