Fault detection and isolation are two significant problems in process monitoring. However, due to the complicated relationships between the process variables, it becomes a challenging problem to build a model to capture the complicated relationship between process variables and perform fault detection and isolation based on the model. This paper proposes an advanced model, called multi-task long short-term memory (MTLSTM) neural networks, that can capture the most complicated relationships between process variables and a simultaneous fault detection and isolation approach based on MTLSTM neural networks. The proposed simultaneous fault detection and isolation approach takes a sparse autoencoder (SAE) to extract features from the measurements of process variables. Then, a long short-term memory neural network is trained on the extracted features with a multi-task learning strategy. Compared with the traditional multivariate statistical models (MVSM) such as principal component analysis and independent component analysis models, the MTLSTM neural networks can capture the nonlinear autocorrelations of process variables and correlations between process variables and perform fault detection and isolation for an industrial process simultaneously. To demonstrate the advantages and superiority of the proposed simultaneous fault detection and isolation approach, a case study on fault detection and isolation for the penicillin fermentation process is carried out. Case study results show that the proposed approach significantly outperforms existing fault detection and isolation approaches.