Semantic information is often represented as the entities and the relationships among them with conventional semantic models. This approach is straightforward but is not suitable for many posteriori requests in semantic data modeling. In this paper, we propose a meaning-oriented approach to modeling semantic data and establish a graph-based semantic data model. In this approach we use the meanings, i.e., the subjective views of the entities and relationships, to describe the semantic information, and use the semantic graphs containing the meaning nodes and the meta-meaning relations to specify the taxonomy and the compound construction of the semantic concepts. We demonstrate how this meaning-oriented approach can address many important semantic representation issues, including dynamic specialization and natural join.