Even though the multimedia data is ubiquitous on the web, the scarcity of the annotated data and variety of data modalities hinder their usage by multimedia applications. Heterogeneous domain adaptation (HDA) has therefore arisen to address such limitations by facilitating the knowledge transfer between heterogeneous domains. Existing HDA methods only focus on aligning the crossdomain feature distributions and ignore the importance of maximizing the margin among different classes, which may lead to a suboptimal classification performance. To tackle this problem, in this paper, we propose the Prototype-Matching Graph Network (PMGN), which gradually explores the domain-invariant class prototype representations. Specifically, we build an end-to-end Graph Prototypical Network, which computes the class prototypes through multiple layers of edge learning, node aggregation, and discrepancy minimization. Our framework utilizes the Swap training strategy to provide adequate supervision for training the edge learning component. Moreover, the proposed PMGN can be equipped with the clustering module that utilises the KL-divergence as a distance metric to reduce the distribution difference between the source and target data. Extensive experiments on three HDA tasks (i.e. object recognition, text-to-image classification, and text categorization) demonstrate the superiority of our approach over the state-of-theart HDA methods. CCS CONCEPTS • Computing methodologies → Transfer learning.