With a mashup network in which a link indicates that two applications are mashupable, building a mashup can be simplified into network navigation. This paper presents an approach that constructs a Web mashup network by learning a semantic Bayesian network using a semi-supervised learning method. An RDF model is defined to describe attributes and activities of applications. To process all information sources on the Semantic Web, a semantic Bayesian network (sBN) is proposed where a semantic sub graph template defined using a SPARQL query is used to describe the information about the graph structure. The sBN offers more powerful abilities to process the information sources on Semantic Web, especially the graph structure. To improve the learning performance, a semi-supervised learning method that makes use of both labeled and unlabeled data is proposed. We ran the approach on a data set containing 100 applications collected from the website Programmableweb.com and 3077 links checked manually. The results show that the approach outperforms the PRL and the rule-based methods, and the semi-supervised learning method achieved big improvements in recall and, compared with the direct learning method.