Quality prediction, as the basis of quality control, is dedicated to predicting quality indices of the manufacturing process. In recent years, data-driven deep learning methods have received a lot of attention due to their accuracy, robustness, and convenience for the prediction of quality indices. However, the existing studies mainly focus on the quality prediction of a single machine, while ignoring dependency relationships among multiple machines in multistage manufacturing process. To tackle the above issues, a novel path enhanced bidirectional graph attention network (PGAT) is proposed in this article. PGAT models the dependencies among machines into directed graphs and introduces graph attention network to encode the dependencies. Nonetheless, it is difficult for graph neural networks to encode long-distance dependencies. Hence, dependency path information is introduced into the features of machines. Moreover, in order to solve the label noise problem that often occurs in actual industrial dataset, a masked loss function is devised. With its help, batch training with noisy labels can be achieved, which improves the training efficiency. Furthermore, experiments are conducted on a public quality prediction dataset collected from an actual production line. PGAT achieves the state-of-the-art results on this dataset, which confirms the effectiveness of PGAT. Additionally, the experimental results demonstrate the critical role of modeling dependency relationships among machines.