Industrial processes are specialized and intricate systems. Current intelligent fault diagnosis methods do not take into account the interactions between individual units and variables, instead using only the temporal or Euclidean geometric space characteristics of industrial process data. How to utilize the complex relationship between variables for fault diagnosis remains an issue to be solved. This study proposed a fault diagnosis framework based on the deep spatiotemporal fusion graph convolutional network (DSTFGCN) for graph representation learning of correlations between variables. First, the maximum information coefficient was introduced to represent the complex correlation between variables in the graph signal construction process. Second, to effectively extract spatiotemporal features from the data, the graph convolutional network (GCN) and the convolutional neural network (CNN) were introduced into the DSTFGCN for mining complex spatial features in the data, and the long short-term memory (LSTM) network was employed to capture the evolution of multivariate time series. Consequently, the fault detection and false-positive rates of the proposed model were, respectively, 94.45% and 0.22% in the Tennessee Eastman Process (TEP), whereas the rates were, respectively, 99.61% and 0.07% on the Three-Phase Flow Facility (TPFF) datasets. These experimental results demonstrate the excellent performance and robustness of the proposed model, compared to those of both machine learning and deep learning models.