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This paper proposes a Local Variable-Weights RBF Network (LVW-RBFN) with the aim to address the problem of modeling and prediction of nonlinear time series. The proposed model is a four layered RBFN comprising of input layer, hidden layer, weight layer and output layer. The LVW-RBFN is an enhanced type of RBF network, in which the constant weights that connect the hidden layer with the output layer in the standard RBFN are replaced by functions of the RBFN's inputs computed via the weight layer. This model has the merit of making usage of more linear parameters and learning the dynamic of nonlinear time series through the hidden and weight layers. An offline optimization technique known as Structured Nonlinear Parameter Optimization Method (SNPOM) was used to estimate the model. Simulation results for the modeling and prediction of some nonlinear time-series show the feasibility and effectiveness of the proposed model.