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The methodology of modeling and analyzing of a knowledge network are discussed in this article. Two steps will be taken to establish the model of a knowledge network for a scientific organization. Based no the network model, the density, betweenness centrality and structure expression analysis will be conducted. The calculation result of the density provides an objective indicator for the researchers to compare with two scientific organizations which are similar in scale. In addition, the betweenness centrality and the successive reduction method identify the level which determines whether the node is important or not. Furthermore, with the clique analysis and the hierarchy cluster method, we achieve the goal to express the structure of the network, which is critical for further study. At last, a numeric example based on the data from Shanghai Institution for Science of Science confirms the feasibility of the methodology of modeling and analysis.