Accurate mine pressure prediction is essential for understanding roof–support interaction and supporting intelligent monitoring in fully mechanized longwall mining. In underground production, hydraulic-support pressure sensors provide continuous pressure sequences that reflect the mechanical response of the support–roof system. However, these sequences are affected by local mining disturbances, missing records, abnormal zero-value segments, nonstationary fluctuations, and periodic weighting, which make future pressure forecasting challenging. To address this issue, an LSTM–Transformer hybrid model is proposed for hydraulic-support pressure forecasting. The LSTM module extracts local nonlinear pressure-evolution features from recent historical windows, whereas the Transformer module captures temporal dependencies and periodic pressure patterns through global sequence modeling. Support-wise experiments were conducted using field monitoring data from Yili No. 1 Mine, and the pressure sequence of each support was processed independently to avoid mixing information from different support locations. In the representative test case, the proposed model achieved an R² of 0.971 and reduced the MAE to 0.471 MPa, while improving the phase consistency of predicted pressure peaks. Further analysis indicates that sufficient historical data coverage is necessary to capture complete pressure-evolution cycles, and that the 25-step forecasting case maintains stable accuracy for short-term mine pressure estimation. These findings demonstrate the feasibility of the proposed approach for hydraulic-support pressure prediction under the monitored conditions of the studied working face.