Gene ontology analysis has become a popular and important tool in bioinformatics study, and current ontology analyses are mainly conducted in individual gene or a gene list. However, recent molecular network analysis reveals that the same list of genes with different interactions may perform different functions. Therefore, it is necessary to consider molecular interactions to correctly and specifically annotate biological networks. Here, we propose a novel Network Ontology Analysis (NOA) method to perform gene ontology enrichment analysis on biological networks. Specifically, NOA first defines link ontology that assigns functions to interactions based on the known annotations of joint genes via optimizing two novel indexes 'Coverage' and 'Diversity'. Then, NOA generates two alternative reference sets to statistically rank the enriched functional terms for a given biological network. We compare NOA with traditional enrichment analysis methods in several biological networks, and find that: (i) NOA can capture the change of functions not only in dynamic transcription regulatory networks but also in rewiring protein interaction networks while the traditional methods cannot and (ii) NOA can find more relevant and specific functions than traditional methods in different types of static networks. Furthermore, a freely accessible web server for NOA has been developed at http://www.aporc.org/noa/.