Affected by factors such as instrument failure, mud invasion, borehole collapse, and incomplete logging data acquisition during secondary development of new layers in mature fields, neutron logging curves in some depth intervals are often distorted or missing, which directly affects the accuracy of reservoir evaluation. To address the difficulty of traditional methods in capturing the correlation features among multiple well logging curves, this paper proposes a neutron logging curve reconstruction method that integrates a Graph Convolutional Neural Network (GCN), a Bidirectional Gated Recurrent Unit (BiGRU), and a Multi-Head Attention (MHA) mechanism. In the proposed method, the GCN is employed to characterize the correlations among multiple well logging curves, the BiGRU is used to model the bidirectional sequential features of logging data along the depth direction, and the MHA mechanism is introduced to enhance the model's focus on important features, thereby improving the reconstruction accuracy of neutron logging curves. Lithofacies-constrained experiments and comparative model evaluations are conducted using multi-well logging data, which verify that the incorporation of formation lithofacies indicators effectively enhances the reconstruction capability of the proposed model. The proposed model is compared with several baseline models, including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Bidirectional Gated Recurrent Unit (BiGRU), and the GCN-BiGRU model. The evaluation results demonstrate that the proposed method significantly outperforms the comparison models across multiple performance metrics. Practical applications of reconstructed logging curves further confirm that the proposed method achieves high accuracy and strong applicability in neutron logging curve reconstruction.