A productivity simulation for hydraulically fractured wells with complex fracture geometry involves a heavy computational burden and is therefore not suitable for engineering-scale fracture-optimization designs and production-analysis applications. This paper develops a productivity-prediction surrogate model based on a deep convolution–bidirectional gated recurrent unit temporal network (DC-BiGRU) framework where a deep convolutional neural network is used to extract features from fracture images, while a BiGRU model was designed to fully capture valuable information from the production sequence. Some additional inputs, e.g., cluster spacing and stage spacing, that account for different fracture-placement designs in horizontal wells were also considered. A large number of shale-gas production data samples at different times were generated using a fractured-horizontal-well productivity simulator under diverse hydraulic-fracture geometries and bottom-hole flowing pressures. The surrogate model had relative errors below 10% with an average error of about 6%. Compared to high-fidelity capacity prediction simulators, the computational efficiency of the deep learning surrogate models was improved by two to three orders of magnitude. The runtime of the high-fidelity numerical simulator was about 20 min, while the surrogate model, which was run on an NVIDIA Tesla P100 GPU (NVIDIA, Santa Clara, CA, USA), took less than 1 s, which is almost negligible. The proposed surrogate model resolved the low efficiency of the productivity simulation for complex-fracture hydraulic fracturing wells in unconventional reservoirs, enabling rapid dynamic forecasting of fractured-well productivity.