CircRNA has been shown to be involved in the occurrence of many diseases. Several computational frameworks have been proposed to identify circRNA-disease associations. Despite the existing computational methods have obtained considerable successes, these methods still require to be improved as their performance may degrade due to the sparsity of the data and the problem of memory overflow. We develop a novel computational framework called LGCDA to predict circRNA-disease associations by fusing local and global features to solve the above mentioned problems. First, we construct closed local subgraphs by using k-hop closed subgraph and label the subgraphs to obtain rich graph pattern information. Then, the local features are extracted by using graph neural network (GNN). In addition, we fuse Gaussian interaction profile (GIP) kernel and cosine similarity to obtain global features. Finally, the score of circRNA-disease associations is predicted by using the multilayer perceptron (MLP) based on local and global features. We perform five-fold cross validation on five datasets for model evaluation and our model surpasses other advanced methods.