Abstract: Fuzzy graphs are widely applied in the modeling and analysis of systems. However, existing fuzzy graph-theoretic constructs are unsuitable for the analysis of the directed relationships between sets of elements. In this paper, a new fuzzy graph, the fuzzy metagraph, is discussed, which describes the relationships between sets of fuzzy elements, but not single fuzzy element, and offers some distinct advantages both for graphical visualization of systems as well as for formal analysis of system structure. The paper emphasizes on analyzing the properties of the fuzzy metagraph, especially the properties of its adjacency matrix, which are the basis of researches and applications of fuzzy metagraphs. Fuzzy metagraphs have wide application prospect in fuzzy rule management and system modeling.