Solving a chaotic problem is one of the application field in studying the characteristics of a nonlinear dynamical system, and actually, many real-world applications are related with a chaotic problem. In order to characterize the chaotic system, deriving the relationship between the linearity and the nonlinearity of the system is necessary, however, determining the mathematical description of a real-world chaotic system is still difficult due to insufficient basic physical phenomena. It is therefore, artificial neural networks approach is developed recently. Multi-step ahead prediction of time series problem is one of the most challenging issues for machine learning methods to solve the chaotic data prediction, especially for its higher prediction rates. In this paper, a modified Radial Basis Function Neural Network (RBFNN) with Extreme Learning Mechanism (ELM) is developed and being tested for a prediction of the future state of a chaotic problem. Experiment results show that the proposed method could provide the optimum RBF parameters with more simple but precise prediction method for up to 60 steps ahead.