The recognition of circRNA-disease association is the key of disease diagnosis and treatment, and it is of great significance for exploring the pathogenesis of complex diseases. Computational methods can predict the potential disease-related circRNAs quickly and accurately. Based on the hypothesis that circRNA with similar function tends to associate with similar disease, GCNCDA model is proposed to effectively predict the potential association between circRNAs and diseases by combining FastGCN algorithm. The performance of the model was verified by cross-validation experiments, different feature extraction algorithm and classifier models comparison experiments. Furthermore, 16, 15 and 17 of the top 20 candidate circRNAs with the highest prediction scores in disease including breast cancer, glioma and colorectal cancer were respectively confirmed by relevant literature and databases. It is anticipated that GCNCDA model can give priority to the most promising circRNA-disease associations on a large scale to provide reliable candidates for further biological experiments. Numerous evidences indicate that Circular RNAs (circRNAs) are widely involved in the occurrence and development of diseases. Identifying the association between circRNAs and diseases plays a crucial role in exploring the pathogenesis of complex diseases and improving the diagnosis and treatment of diseases. However, due to the complex mechanisms between circRNAs and diseases, it is expensive and time-consuming to discover the new circRNA-disease associations by biological experiment. Therefore, there is increasingly urgent need for utilizing the computational methods to predict novel circRNA-disease associations. In this study, we propose a computational method called GCNCDA based on the deep learning Fast learning with Graph Convolutional Networks (FastGCN) algorithm to predict the potential disease-associated circRNAs. Specifically, the method first forms the unified descriptor by fusing disease semantic similarity information, disease and circRNA Gaussian Interaction Profile (GIP) kernel similarity information based on known circRNA-disease associations. The FastGCN algorithm is then used to objectively extract the high-level features contained in the fusion descriptor. Finally, the new circRNA-disease associations are accurately predicted by the Forest by Penalizing Attributes (Forest PA) classifier. The 5-fold cross-validation experiment of GCNCDA achieved 91.2% accuracy with 92.78% sensitivity at the AUC of 90.90% on circR2Disease benchmark dataset. In comparison with different classifier models, feature extraction models and other state-of-the-art methods, GCNCDA shows strong competitiveness. Furthermore, we conducted case study experiments on diseases including breast cancer, glioma and colorectal cancer. The results showed that 16, 15 and 17 of the top 20 candidate circRNAs with the highest prediction scores were respectively confirmed by relevant literature and databases. These results suggest that GCNCDA can effectively predict potential circRNA-disease associations and provide highly credible candidates for biological experiments.