Since the iron-making process is performed in complicated environments and controlled by operators, observation labeling is difficult and time-consuming. Therefore, unsupervised fault detection methods are a promising research topic. Recently, an unsupervised graph-based change point detection method has been introduced, and the graph of observations is constructed by the minimum spanning tree. In this paper, a novel fault detection method based on the graph for an iron-making process is proposed, and a weight calculation method for constructing the minimum spanning tree is introduced. The Euclidean distance and Mahalanobis distance are combined to calculate the weights in the minimum spanning tree, which contain important relations of variables. The distance calculation method is determined by the correlation coefficients of variables. Each testing observation is set as a change point candidate, and a change point candidate divides the observations into two groups. The number of a special type of edge in the minimum spanning tree is used as a fault detection statistic. That special edge connects two observations from two different groups. The minimum number of that type of edge corresponding to the change point candidate is a true change point. Finally, numerical simulation is used to test the power of the proposed method, and a real iron-making process including low stock, cooling, and slip faults is implemented to illustrate the effectiveness of fault detection in industrial processes.