Link prediction is a technique for predicting future or missing relationships between entities based on current network information. Recent studies on link prediction in multiplex networks have improved prediction accuracy by considering inter-layer similarity, but they do not fully exploit the distinct topological information present in each individual network layer. Therefore, this paper proposes a link prediction algorithm based on a layer attention mechanism for multiplex networks, called LATGCN, which simultaneously considers both inter-layer and intra-layer information. Firstly, it uses two-layer GCN to capture the intra-layer embedding representation of a multiplex network. Secondly, it employs the layer attention mechanism to find the layer importance score of each layer of the multiplex network, and utilizes the layer importance scores to weight the intra-layer information according to the difference in importance. Thirdly, we design an embedding representation fusion module to integrate the intra-layer embedding representation and global embedding representation. Finally, experimental results on four real-world social networks and two biological networks show that LATGCN outperforms all compared methods across four evaluation metrics, demonstrating its effectiveness for link prediction.