Air Traffic Flow Management (ATFM) delay can quantitatively reflect the congestion caused by the imbalance between capacity and demand in an airspace network. Furthermore, it is an important parameter for the ex-post analysis of airspace congestion and the effectiveness of ATFM strategy implementation. If ATFM delays can be predicted in advance, the predictability and effectiveness of ATFM strategies can be improved. In this paper, a short-term ATFM delay regression prediction method is proposed for the characteristics of the multiple sources, high dimension, and complexity of ATFM delay prediction data. The method firstly constructs an ATFM delay prediction network model, specifies the prediction object, and proposes an ATFM delay prediction index system by integrating common flow control information. Secondly, an ATFM delay prediction method based on feature extraction modules (including CNN, TCN, and attention modules), a heuristic optimization algorithm (sparrow search algorithm (SSA)), and a prediction model (LSTM) are proposed. The method constructs a CNN-LSTM-ATT model based on SSA optimization and a TCN-LSTM-ATT model based on SSA optimization. Finally, four busy airports and their major waypoints in East China are selected as the ATFM delay prediction network nodes for example validation. The experimental results show that the MAEs of the two models proposed in this paper for ATFM delay regression prediction are 4.25 min and 4.38 min, respectively. Compared with the CNN-LSTM model, the errors are reduced by 2.71 min and 2.59 min, respectively. Compared with the TCN-LSTM model, the times are 3.68 min and 3.55 min, respectively. In this paper, two improved LSTM models are constructed to improve the prediction accuracy of ATFM delay duration so as to provide support for the establishment of an ATFM delay early warning mechanism, further improve ATFM delay management, and enhance resource allocation efficiency.