Lots of experimental studies have revealed the significant associations between lncRNAs and diseases. Identifying accurate associations will provide a new perspective for disease therapy. Calculation-based methods have been developed to solve these problems, but these methods have some limitations. In this paper, we proposed an accurate method, named MLGCNET, to discover potential lncRNA-disease associations. Firstly, we reconstructed similarity networks for both lncRNAs and diseases using top k similar information, and constructed a lncRNA-disease heterogeneous network (LDN). Then, we applied Multi-Layer Graph Convolutional Network on LDN to obtain latent feature representations of nodes. Finally, the Extra Trees was used to calculate the probability of association between disease and lncRNA. The results of extensive 5-fold cross-validation experiments show that MLGCNET has superior prediction performance compared to the state-of-the-art methods. Case studies confirm the performance of our model on specific diseases. All the experiment results prove the effectiveness and practicality of MLGCNET in predicting potential lncRNA-disease associations.