Prediction of subsurface oil reservoir pressure are critical to hydrocarbon production. However, the accurate pressure estimation faces great challenges due to the complexity and uncertainty of reservoir. The underground seepage flow and petrophysical parameters (permeability and porosity) are important but difficult to measure in oilfield. Deep learning methods have been successfully used in reservoir engineering and oil & gas production process. In this study, the effective but inaccessible subsurface seepage fields are not used, only the spatial coordinates and temporal information are selected as model input to predict reservoir pressure. A stacked GRU-based deep learning model is proposed to map the relationship between spatio-temporal data and reservoir pressure. The proposed deep learning method is verified by using a three-dimensional reservoir model, and compared with commonly-used methods. The results show that the stacked GRU model has a better performance and higher accuracy than other deep learning or machine learning methods in pressure prediction.