In recent years, heterogeneous graphs, a complex graph structure that can express multiple types of nodes and edges, have been widely used for modeling various real-world scenarios. As a powerful analysis tool, heterogeneous graph neural networks (HGNNs) can effectively mine the information and knowledge in heterogeneous graphs. However, designing an excellent HGNN architecture requires a lot of domain knowledge and is a time-consuming and laborious task. Inspired by neural architecture search (NAS), some works on homogeneous graph NAS have emerged. However, there are few works on heterogeneous graph NAS. In addition, the hyperparameters related to the HGNN architecture are also important factors affecting its performance in downstream tasks. Manually tuning hyperparameters is also a tedious and inefficient process. To solve the above problems, we propose a novel search (HG-Search for short) algorithm specifically for HGNNs, which achieves fully automatic architecture design and hyperparameter tuning. Specifically, we first design a search space for HG-Search, composed of two parts: HGNN architecture search space and hyperparameter search space. Furthermore, we propose a multi-stage search (MS-Search for short) module and combine it with the policy gradient search (PG-Search for short). Experiments on real-world datasets show that this method can design HGNN architectures comparable to those manually designed by humans and achieve automatic hyperparameter tuning, significantly improving the performance in downstream tasks. The code and related datasets can be found at https://github.com/dawn-creator/HG-Search.