A major challenge in the post-genomic era is to determine protein function on a proteomic scale. There are only less than half of the actual functional annotations available for a typical proteome. The recent high-throughput bio-techniques have provided us large-scale protein-protein interaction data, and many studies have shown that function prediction from protein-protein interaction data is a promising way since proteins are likely to collaborate for a common purpose. However, the protein interaction data is very noisy, which makes the task very challenging. In this paper, we propose a distance matrix based on the small world property of the protein-protein interaction network. It measures the reliability of edges and filter the noise in the network. In addition, an ANN (Artificial Neural Network) based method was designed to predict protein functions on the basis of integration of several protein interaction data sets. We tested our approach with MIPS functional categories. The experiential results show that our approach has better performance than other existing methods in terms of precision and recall.