In skeleton-based human action recognition methods, human behaviours can be analysed through temporal and spatial changes in the human skeleton. Skeletons are not limited by clothing changes, lighting conditions, or complex backgrounds. This recognition method is robust and has aroused great interest; however, many existing studies used deep-layer networks with large numbers of required parameters to improve the model performance and thus lost the advantage of less computation of skeleton data. It is difficult to deploy previously established models to real-life applications based on low-cost embedded devices. To obtain a model with fewer parameters and a higher accuracy, this study designed a lightweight frame-level joints adaptive graph convolutional network (FLAGCN) model to solve skeleton-based action recognition tasks. Compared with the classical 2s-AGCN model, the new model obtained a higher precision with 1/8 of the parameters and 1/9 of the floating-point operations (FLOPs). Our proposed network characterises three main improvements. First, a previous feature-fusion method replaces the multistream network and reduces the number of required parameters. Second, at the spatial level, two kinds of graph convolution methods capture different aspects of human action information. A frame-level graph convolution constructs a human topological structure for each data frame, whereas an adjacency graph convolution captures the characteristics of the adjacent joints. Third, the model proposed in this study hierarchically extracts different levels of action sequence features, making the model clear and easy to understand; further, it reduces the depth of the model and the number of parameters. A large number of experiments on the NTU RGB + D 60 and 120 data sets show that this method has the advantages of few required parameters, low computational costs, and fast speeds. It also has a simple structure and training process that make it easy to deploy in real-time recognition systems based on low-cost embedded devices.