Long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) are two typical types of non-coding RNAs that interact and play important regulatory roles in many animal organisms. Exploring the unknown interactions between lncRNAs and miRNAs contributes to a better understanding of their functional involvement. Currently, studying the interactions between lncRNAs and miRNAs heavily relies on laborious biological experiments. Therefore, it is necessary to design a computational method for predicting lncRNA-miRNA interactions. In this work, we propose a method called MPGK-LMI, which utilizes a graph attention network (GAT) to predict lncRNA-miRNA interactions in animals. First, we construct a meta-path similarity matrix based on known lncRNA-miRNA interaction information. Then, we use GAT to aggregate the constructed meta-path similarity matrix and the computed Gaussian kernel similarity matrix to update the feature matrix with neighbourhood information. Finally, a scoring module is used for prediction. By comparing with three state-of-the-art algorithms, MPGK-LMI achieves the best results in terms of performance, with AUC value of 0.9077, AUPR of 0.9327, ACC of 0.9080, F1-score of 0.9143 and precision of 0.8739. These results validate the effectiveness and reliability of MPGK-LMI. Additionally, we conduct detailed case studies to demonstrate the effectiveness and feasibility of our approach in practical applications. Through these empirical results, we gain deeper insights into the functional roles and mechanisms of lncRNA-miRNA interactions, providing significant breakthroughs and advancements in this field of research. In summary, our method not only outperforms others in terms of performance but also establishes its practicality and reliability in biological research through real-case analysis, offering strong support and guidance for future studies and applications.