Accumulated evidence of biological clinical trials has shown that long non-coding RNAs (lncRNAs) are closely related to the occurrence and development of various complex human diseases. Research works on lncRNA–disease relations will benefit to further understand the pathogenesis of human complex diseases at the molecular level, but only a small proportion of lncRNA–disease associations has been confirmed. Considering the high cost of biological experiments, exploring potential lncRNA–disease associations with computational approaches has become very urgent. In this study, a model based on closest node weight graph of the spatial neighborhood (CNWGSN) and edge attention graph convolutional network (EAGCN), LDA-EAGCN, was developed to uncover potential lncRNA–disease associations by integrating disease semantic similarity, lncRNA functional similarity, and known lncRNA–disease associations. Inspired by the great success of the EAGCN method on the chemical molecule property recognition problem, the prediction of lncRNA–disease associations could be regarded as a component recognition problem of lncRNA–disease characteristic graphs. The CNWGSN features of lncRNA–disease associations combined with known lncRNA–disease associations were introduced to train EAGCN, and correlation scores of input data were predicted with EAGCN for judging whether the input lncRNAs would be associated with the input diseases. LDA-EAGCN achieved a reliable AUC value of 0.9853 in the ten-fold cross-over experiments, which was the highest among five state-of-the-art models. Furthermore, case studies of renal cancer, laryngeal carcinoma, and liver cancer were implemented, and most of the top-ranking lncRNA–disease associations have been proven by recently published experimental literature works. It can be seen that LDA-EAGCN is an effective model for predicting potential lncRNA–disease associations. Its source code and experimental data are available at https://github.com/HGDKMF/LDA-EAGCN.