Abstract Heterogeneous domain adaptation (HDA) aims to exploit knowledge from a heterogeneous source domain to improve the learning performance in a target domain. Since the feature spaces of the source and target domains are different, the transferring of knowledge is extremely diffificult. In this paper, we propose a novel semi-supervised algorithm for HDA by exploiting the theory of optimal transport (OT), a powerful tool originally designed for aligning two different distributions. To match the samples between heterogeneous domains, we propose to preserve the semantic consistency between heterogeneous domains by incorporating label information into the entropic Gromov-Wasserstein discrepancy, which is a metric in OT for different metric spaces, resulting in a new semi-supervised scheme. Via the new scheme, the target and transported source samples with the same label are enforced to follow similar distributions. Lastly, based on the Kullback-Leibler metric, we develop an ef- fificient algorithm to optimize the resultant problem. Comprehensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.