A modified RBF (radial basis function)-based neural network is proposed for network anomaly detection. Special attention is given to the determination of the parameters of the hidden layer. We propose a novel grid-based approach to compress and cluster the training data. The number, center and radii of the RBFs are determined according to the clustering result. At the detecting stage, we expand each input node with a sigmoid function to meet the type of input data. Experimental result on KDD 99 intrusion detection datasets shows that our RBF based IDS has high detection rate while maintaining a low false positive rate. It also shows the remarkable ability of our IDS to detect new type of attacks.