In this paper, we introduce an innovative fuzzy clustering model that includes some prior knowledge about the data. The prior knowledge is the data correlations expressed in a form of graph. Specifically, in this new model, we add a graph regularization term to the objective function of Fuzzy C-Mean (FCM) to fine-tune the final clustering result. By doing so, when we conduct fuzzy clustering to classify data according to some unary features, the priors about binary relations in the data are also well addressed. The new model is a general optimization problem that can be solved by Alternating Direction Method of Multipliers efficiently. Verified by experimental results, the proposed model is effective to improve the performance of fuzzy clustering and the efficiency of FCM based image segmentation.