Predicting shale gas production under different geological and fracturing conditions in the fractured shale gas reservoirs is the foundation of optimizing the fracturing parameters, which is crucial to effectively exploit shale gas. We present a multi-layer perceptron (MLP) network and a long short-term memory (LSTM) network to predict shale gas production, both of which can quickly and accurately forecast gas production. The prediction performances of the networks are comprehensively evaluated and compared. The results show that the MLP network can predict shale gas production by geological and fracturing reservoir parameters. The average relative error of the MLP neural network is 2.85%, and the maximum relative error is 12.9%, which can meet the demand of engineering shale gas productivity prediction. The LSTM network can predict shale gas production through historical production under the constraints of geological and fracturing reservoir parameters. The average relative error of the LSTM neural network is 0.68%, and the maximum relative error is 3.08%, which can reliably predict shale gas production. There is a slight deviation between the predicted results of the MLP model and the true values in the first 10 days. This is because the daily production decreases rapidly during the early production stage, and the production data change greatly. The largest relative errors of LSTM in this work on the 10th, 100th, and 1000th day are 0.95%, 0.73%, and 1.85%, respectively, which are far lower than the relative errors of the MLP predictions. The research results can provide a fast and effective mean for shale gas productivity prediction.