Influenza viruses rapidly evolve to evade previously acquired human immunity. Maintaining vaccine efficacy necessitates continuous monitoring of antigenic differences among strains. Traditional serological methods for assessing these differences are labor-intensive and time-consuming, highlighting the need for efficient computational approaches. This paper proposes MetaFluAD, a meta-learning-based method designed to predict quantitative antigenic distances among strains. This method models antigenic relationships between strains, represented by their hemagglutinin (HA) sequences, as a weighted attributed network. Employing a graph neural network (GNN)-based encoder combined with a robust meta-learning framework, MetaFluAD learns comprehensive strain representations within a unified space encompassing both antigenic and genetic features. Furthermore, the meta-learning framework enables knowledge transfer across different influenza subtypes, allowing MetaFluAD to achieve remarkable performance with limited data. MetaFluAD demonstrates excellent performance and overall robustness across various influenza subtypes, including A/H3N2, A/H1N1, A/H5N1, B/Victoria, and B/Yamagata. MetaFluAD synthesizes the strengths of GNN-based encoding and meta-learning to offer a promising approach for accurate antigenic distance prediction. Additionally, MetaFluAD can effectively identify dominant antigenic clusters within seasonal influenza viruses, aiding in the development of effective vaccines and efficient monitoring of viral evolution.