The number of graph neural network (GNN) architectures has increased rapidly due to the growing adoption of graph analysis. Although we use GNNs in wide application scenarios, it is a laborious task to design/select optimal GNN architectures in diverse graphs. To reduce human efforts, graph neural architecture search (Graph NAS) has been used to search for a sub-optimal GNN architecture that combines existing components. However, existing Graph NAS methods lack explainability to understand the reasons why the model architecture is selected because they use complex search space and neural models to select architecture. Therefore, we propose an explainable Graph NAS method, called ExGNAS, which consists of (i) a simple search space that can adapt to various graphs and (ii) a search algorithm with Monte-Carlo tree that makes the decision process explainable. The combination of our search space and algorithm achieves finding accurate GNN models and the important functions within the search space. We comprehensively evaluate ExGNAS compared with four state-of-the-art Graph NAS methods in twelve graphs. Our experimental results show that ExGNAS achieves high average accuracy and efficiency; improving accuracy up to 26.1% and reducing run time up to 88%. Furthermore, we show the effectiveness of explainability by questionnaire-based user study and architecture analysis.