Heterogeneous Graph Neural Networks (HGNNs), have demonstrated excellent capabilities in processing heterogeneous information networks. Self-supervised learning on heterogeneous graphs, especially contrastive self-supervised strategy, shows great potential when there are no labels. However, this approach requires the use of carefully designed graph augmentation strategies and the selection of positive and negative samples. Determining the exact level of similarity between sample pairs is non-trivial.To solve this problem, we propose a novel self-supervised Heterogeneous graph neural network with Optimal Transport (HGOT) method which is designed to facilitate self-supervised learning for heterogeneous graphs without graph augmentation strategies. Different from traditional contrastive self-supervised learning, HGOT employs the optimal transport mechanism to relieve the laborious sampling process of positive and negative samples. Specifically, we design an aggregating view (central view) to integrate the semantic information contained in the views represented by different meta-paths (branch views). Then, we introduce an optimal transport plan to identify the transport relationship between the semantics contained in the branch view and the central view. This allows the optimal transport plan between graphs to align with the representations, forcing the encoder to learn node representations that are more similar to the graph space and of higher quality. Extensive experiments on four real-world datasets demonstrate that our proposed HGOT model can achieve state-of-the-art performance on various downstream tasks. In particular, in the node classification task, HGOT achieves an average of more than 6% improvement in accuracy compared with state-of-the-art methods.