Gas well productivity prediction is an important task in gas field development. In contrast, shale gas production is influenced by many factors in geology and production with strong nonlinear characteristics. Traditional mechanism-based productivity prediction methods are difficult to comprehensively and accurately characterize multi-dimensional and multi-structural types of productivity influencing factors, and it is difficult to quickly solve the production dynamics after shale gas fracturing. To address this problem, based on LSTM and DNN, a novel fitting function-neural network synergistic model for dynamic production productivity prediction of shale gas wells was proposed in this paper. Firstly, the data set was constructed by reorganizing the data dimensions, mixing the time-series parameters such as production and pressure in the early stage of the target well with the static productivity control parameters such as fluid intensity, sand addition intensity, total gas content, brittle mineral content, etc., in order to achieve the prediction of the production curve in the late stage of the target well. Second, based on the real daily gas production data in the field, the Arps productivity curve fitting model was used to filter the productivity data of neighboring wells in the same block to indirectly add a weak physical constraint containing the law of decreasing productivity; based on the strong correlation between single-day production time and production under actual working conditions, a strong physical constraint was added inside the neural network model to improve the productivity time series prediction accuracy and local stability of this model. This improves the prediction accuracy and local stability of the model. Based on this model, a shale gas block in China was predicted to have a future production curve, and the prediction results were cross-validated by k-fold Method. Among them, the effects of neural network model parameters, productivity control parameters and time step on the model accuracy were discussed separately. The results show that the model in this paper has a high accuracy rate. With a small sample of production data from neighboring wells, the model can still capture more production characteristics by using static capacity control parameters such as fluid intensity and pre-production and pressure profiles of the target wells. This study results in this paper provide some guidance for the evaluation of fracturing effect of old wells and the optimization of production parameters of new wells.