Most recent developments of computer sciences, such as web services, Grid, peer-to-peer, and mobile computing, are network-based computing. Their applicability depends on the availability of the underlying network bandwidth. However, network resources are shared and the available network bandwidth varies with time. There is no satisfactory solution available for network performance predictions. This lack of prediction limits the applicability of network-based computing, especially for Grid computing where concurrent remote processing is essential. In this study, we propose an Artificial Neural Network (ANN) based approach for network performance prediction. The ANN mechanism has been tested on classical trace files and compared with the well-known system NWS (Network Weather Service) for performance. Experimental results show the ANN approach always provides an improved prediction over that of NWS. ANN has a real potential in network computing.