With the development of gas sensor arrays and computational technology, machine olfactory systems have been widely used in environmental monitoring, medical diagnosis, and other fields. The reliable and stable operation of gas sensing systems depends heavily on the accuracy of the sensors outputs. Therefore, the realization of accurate gas sensor array fault diagnosis is essential to monitor the working status of sensor arrays and ensure the normal operation of the whole system. The existing methods extract features from a single dimension and require the separate training of models for multiple diagnosis tasks, which limits diagnostic accuracy and efficiency. To address these limitations, for this study, a novel fault diagnosis network based on multi-dimensional feature fusion, an attention mechanism, and multi-task learning, MAM-Net, was developed and applied to gas sensor arrays. First, feature fusion models were applied to extract deep and comprehensive features from the original data in multiple dimensions. A residual network equipped with convolutional block attention modules and a Bi-LSTM network were designed for two-dimensional and one-dimensional signals to capture spatial and temporal features simultaneously. Subsequently, a concatenation layer was constructed using feature stitching to integrate the fault details of different dimensions and avoid ignoring useful information. Finally, a multi-task learning module was designed for the parallel learning of the sensor fault diagnosis to effectively improve the diagnosis capability. The experimental results derived from using the proposed framework on gas sensor datasets across different amounts of data, balanced and unbalanced datasets, and different experimental settings show that the proposed framework outperforms the other available methods and demonstrates good recognition accuracy and robustness.