It has been shown by Roger Jang in his paper titled "Adaptive-network-based fuzzy inference systems" that the Adaptive Network based Fuzzy Inference System can model nonlinear functions, identify nonlinear components in a control system, and predict a chaotic time series. The system use hybrid-learning procedure which employs the back-propagation-type gradient descent algorithm and the least squares estimator to estimate parameters of the model. However the learning procedure has several shortcomings due to the fact that * There is a harmful and unforeseeable influence of the size of the partial derivative on the weight step in the back-propagation-type gradient descent algorithm. *In some cases the matrices in the least square estimator can be ill-conditioned. *Several estimators are known which dominate, or outperform, the least square estimator. Therefore this thesis develops a new system that overcomes the above problems, which is called the "Faster Adaptive Network Fuzzy Inference System" (FANFIS). The new system in this thesis is shown to significantly out perform the existing method in predicting a chaotic time series , modelling a three-input nonlinear function and identifying dynamical systems. We also use FANFIS to predict five major stock closing prices in New Zealand namely Air New Zealand "A" Ltd., Brierley Investments Ltd., Carter Holt Harvey Ltd., Lion Nathan Ltd. and Telecom Corporation of New Zealand Ltd. The result shows that the new system out performed other competing models and by using simple trading strategy, profitable forecasting is possible.