A fall detection algorithm combining OpenPose with an improved ST-GCN is proposed to address the limitations of low accuracy and the need for pre-defining human skeleton topology graphs of the ST-GCN algorithm in action recognition. The OpenPose algorithm is used to extract the human skeletal keypoint data, which is then input into the improved ST-GCN algorithm for action recognition. The ST-GCN algorithm is improved by introducing an adaptive graph convolution module, which dynamically adjusts the graph structure to enhance the flexibility in feature extraction across different action types; an attention mechanism module is introduced to further improve the recognition performance of the model. Validation on publicly available datasets shows that on the NTU-RGB+D 60 dataset, the top-1 accuracy of X-Sub and X-View is improved by 2.2% and 2.5%, respectively, compared with the baseline; on the Kinetics-Skeleton dataset, the top-1 and top-5 accuracy are improved by 3.1% and 4%, respectively. In addition, the accuracy measured on the self-constructed dataset is improved by 4.7% compared with that before the improvement. The experimental results show that the proposed algorithm meets the requirements of practical applications.