Data mining, the extraction of hidden predictive information from large databases, is a powerful new technology with great potential to help companies focus on the most important information in their data warehouses. One of the most commonly used techniques in data mining, Artificial Neural Networks provide non-linear predictive models that learn through training and resemble biological neural networks in structure. This paper deals with a new adaptive neural network model: a feed-forward neural network with a new activation function called neuron-adaptive activation function. Experiments with function approximation and stock market movement analysis have been conducted to justify the new adaptive neural network model. Experimental results have revealed that the new adaptive neural network model presents several advantages over traditional neuron-fixed feed-forward networks such as much reduced network size, faster learning, and more promising financial analysis.