Providing timely rescue when a fall occurs can greatly reduce fall mortality for older people. With the growing number of single-resided elders, real-time smart fall incident detection has become a new research hotspot. Accuracy, computational complexity and real-time response are key issues to be solved in this topic. A fall detection model that combines an improved Spatial–Temporal Graph Convolutional Network (ST-GCN) with the BlazePose algorithm is proposed in this paper. The computational speed is improved by removing four redundant layers from the ST-GCN network. Meanwhile, an attention mechanism focussing on the key joints involved in the falling action and their correlation is applied in the model, which introduces an Effective SE Block (ESE Block) to the residual structure of ST-GCN. It is achieved by fusing the original features with channel attention weights obtained by global average pooling and fully connected operations for the joint features. The BlazePose algorithm of the mediapipe framework is used to recognise human targets and locate the spatial coordinates of specific joints. Then the spatiotemporal graph features of the human body are extracted by the improved ST-GCN from the temporal and spatial displacements of 30 consecutive frames. Furthermore, fall behaviour is judged by the action type defined by the spatiotemporal graph. The accuracy of the proposed model for public datasets, such as Le2i Fall, Multicam Fall and UR Fall, is 99.29%, 99.22% and 98.64% respectively, which are higher than the Alphapose + ST-GCN model by 9.04%, 20% and 25.2%. Such accuracy is even better than the existing best algorithms by 0.89%, 0.92% and 1.04%. When running on the i5-10200H CPU and the Jetson Nano edge computing device, the Alphapose + ST-GCN model achieves frame rates of 11.42fps and 1.5fps, whilst the frame rates of this paper are up to 24.5fps and 9.37fps. The experimental results fully show that based on BlazePose with the improved ST-GCN makes the fall detection model higher accuracy, faster speed, real-time performance and high compatibility with the Jetson Nano edge computing device.