Human action abnormality detection has been attempted by various sensors for application domains like rehabilitation, healthcare, and assisted living. Since the release of motion sensors that ease the human body skeleton retrieval, skeleton-based human action recognition has recently been an active topic in the area of artificial intelligence. Unlike human action recognition, human action abnormality detection is an emerging field that aims to detect the incorrect action from the same action class. Graph convolutional network has been widely adopted for human action recognition. However, to the best of our knowledge, whether it could be effective for the task of human action abnormality detection has not been attempted. To advance prior work in the emerging field of human action abnormality detection, we propose a novel method that uses graph convolutional network to detect abnormal actions in skeleton data. To validate the effectiveness of our proposed method, we conduct extensive experiments on a public dataset called UI-PRMD. Based on the experimental results, our proposed method achieved superior action abnormality detection performance comparing with existing deep learning methods.