To address the issues of information imbalance and the difficulty in synergistically extracting global and local features during extracorporeal membrane oxygenation (ECMO) fault diagnosis, this paper proposes a model integrating Chebyshev graph convolutional neural networks (ChebyNet) with convolutional neural networks (CNN) (CNN-ChebyNet). This model is applied to ECMO fault diagnosis tasks to efficiently enhance feature extraction accuracy. Firstly, a graph symmetry processing mechanism is introduced into the ChebyNet framework to improve the balance of information flow between nodes. Secondly, by combining ChebyNet’s global modeling capability with CNN’s local temporal feature extraction ability, multidimensional representation of complex fault features is achieved. Finally, through multi-task learning node reconstruction and classification tasks, the perception of latent correlations among samples is enhanced. Experiments on the ECMO blood pump impeller assembly dataset demonstrate that the CNN-ChebyNet model achieves superior performance across multiple comparison methods, with an average diagnostic accuracy exceeding 99%, showcasing outstanding diagnostic capability and stability. Furthermore, ablation experiments validate the effectiveness of each model component in multi-fault identification. In summary, this study provides an effective and feasible technical solution for fault diagnosis in ECMO devices.