The chronological classification of bronze inscriptions is crucial to reconstructing the developmental trajectories of ancient societies. Manual chronological classification methods suffer from inefficiency. Traditional deep learning methods can efficiently process large amounts of data, but they inadequately address the high similarity of glyphs between close eras. In order to overcome the limitations of existing methods, we propose a novel framework integrating multi-task learning, knowledge distillation and graph convolutional networks (MTKD-GCN). First, to take advantage of the consistency of the chronological changes in the composition of Chinese characters and focus on the small changes in glyphs, we introduce an auxiliary glyph recognition task within a multi-task learning framework to jointly extract chronological style features and glyph features. Second, to avoid model converging to suboptimal solutions due to excessive parameter coupling across tasks, we use knowledge distillation to enhance model stability and feature specificity. Third, to address the problem of missing glyphs in chronology, we use a graph convolutional network to enhance label correlation between tasks. In addition, we construct the first Bronze Inscription Chronology Dataset (BCID). The experimental results based on different backbones demonstrate that MTKD-GCN achieves better performance in multiple metrics compared to other methods. In particular, adopting ResNet as the backbone achieves significant performance improvements compared to baseline model, with accuracy, macro-averaged precision and macro F1 score increasing by 2.15%, 10.28%, and 5.04% respectively.