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The estimated ultimate recovery (EUR) of shale gas wells is influenced by many factors, and the accurate prediction still faces certain challenges. As an artificial intelligence algorithm, deep learning yields notable advantages in nonlinear regression. Therefore, it is feasible to predict the EUR of shale gas wells based on a deep-learning algorithm. In this paper, according to geological evaluation data, hydraulic fracturing data, production data and EUR evaluation results of 282 wells in the WY shale gas field, a deep-learning-based algorithm for EUR evaluation of shale gas wells was designed and realized. First, the existing EUR evaluation methods of shale gas wells and the deep feedforward neural network algorithm was systematically analyzed. Second, the technical process of a deep-learning-based algorithm for EUR prediction of shale gas wells was designed. Finally, by means of real data obtained from the WY shale gas field, several different cases were applied to testify the validity and accuracy of the proposed approach. The results show that the EUR prediction with high accuracy. In addition, the results are affected by the variety and number of input parameters, the network structure and hyperparameters. The proposed approach can be extended to other shale fields using the similar technic process.