With the trend towards large-scale structure and complexity in modern chemical processes, it is difficult to describe the system operating status and fault conditions via traditional approaches. In addition, there are obstacles to fault detection research in complex chemical processes due to the characteristics of the equipment hardware used in chemical systems, data collection and handling, strong internal correlations in chemical systems, factors affecting transmission, and randomness and cascade in process failures. Therefore, this paper presents a fault detection method based on horizontal visibility graph (HVG) analysis-integrated complex networks. The data for each variable in the system are regarded as a time series, each time series is modelled into a network by the horizontal visibility algorithm, and each single-layer network corresponding to a time series is abstracted as a node. Meanwhile, the correlation between two single-layer networks is used to characterize the correlation between the corresponding nodes. Moreover, a complex network structure representing the chemical system can be constructed from the correlations. In addition, according to the correlation ratio matrix obtained from the fault state and the normal state, the variance of each node determines the faulty node. Finally, we verify the validity and the effectiveness of the proposed method by applying it to the Tennessee Eastman (TE) process.