Since shale gas is a valuable energy resource, effective planning for its extraction and utilization depends on precise forecasting of gas well production. Conventional models need long computation time, a wide range of geological and fluid data, and suffer from unstable predictions. To develop a low-cost, intelligent, and reliable forecast system for shale gas production, a hybrid Temporal Convolutional Network-Policy Gradient Informer (TCN-PgInformer) model was constructed for multivariate production prediction research. This model is based on the Informer model of its own unique self-attention mechanism, which lowers the temporal complexity of conventional self-attention technique while increasing the model’s accuracy. Meanwhile, to completely avoid the gradient vanishing problem, the dilated convolutions of TCN structure are employed to extract the long-term dependency relationships. Ultimately, a policy gradient (Pg) algorithm is introduced to enhance the parameter training speed. The results indicate that the daily gas production may be accurately predicted by TCN-PgInformer model. A detailed performance comparison was carried out among TCN-PgInformer, CNN, GRU and CNN-LSTM models in the literature. The comparison demonstrates that the suggested TCN-PgInformer model outperforms existing techniques. For four different gas production stages, the MAPE/RMSE error of other models is 2–12 times higher than that of the TCN-PgInformer model, while the R2 accuracy of TCN-PgInformer model can be as high as 1 time higher than other models. Therefore, the designed model has excellent applicability, which offers reference and guidance for shale gas development