Accurate prediction of future trajectories for surrounding vehicles is vital for the safe operation of autonomous vehicles. This study proposes a Lane Graph Transformer (LGT) model with structure-aware capabilities. Its key contribution lies in encoding the map topology structure into the attention mechanism. To address variations in lane information from different directions, four relative positional encoding (RPE) matrices are introduced to capture the local details of the map topology structure. Additionally, two shortest path distance (SPD) matrices are employed to capture distance information between two accessible lanes. The prediction results of the Argoverse 2 dataset indicate that the proposed LGT model can decrease the minimum final displacement error (minFDE6) metric by 60.73% compared to the nearest neighbor model and reduce the b-minFDE6 by 2.65% compared to the baseline LaneGCN model. Furthermore, ablation experiments demonstrated that the consideration of map topology structure led to a 4.24% drop in the b-minFDE6 metric, validating the effectiveness of this model. Our code is publicly available at: https://github.com/dongcaiyin/LGT2024.