With the enhancement of China’s comprehensive national power and the improvement of people’s living standards, health has become the goal that people pursue. While people are thirsty for extensive knowledge and a healthy body, they also pay more attention to the cultivation of elegant temperament and the enjoyment of beauty, and aerobics has become a hot spot for national fitness with its advantages of coordinated and beautiful movements, bright and cheerful rhythm and obvious fitness effects. Aerobics is a new popular fitness sports, from the beginning of development by most fitness enthusiasts, especially it is a women’s favorite. To this end, the characteristics, value, status, and role of aerobics in the public health of all people are discussed, and the problems of poor recognition effect in the existing aerobics difficulty aerobics action recognition methods are proposed to apply the graph convolutional neural network to the aerobics difficulty aerobics action recognition. The video of aerobics is divided into several images, and the background of the aerobics difficult aerobics action image is eliminated, and the gray scale co-generation matrix is set to estimate the local area blur kernel of the difficult action image to correct the visual error of the difficult action image. “change to” The aerobics action is divided into several difficult action images, and the gray-scale symbiosis matrix is set to estimate the local area fuzzy core of the difficult action image, and correct the visual error of the difficult action image. On this basis, the graph convolutional neural network is pre-trained to construct a human-directed spatial-temporal skeleton map, and the human-directed spatial-temporal map representation is modeled with temporal dynamic information to achieve aerobics difficult aerobics action recognition. The experimental results show that the recognition time of the difficult aerobics movements based on the graph convolutional neural network is shorter and the number of false recognitions is less in complex and simple backgrounds, which proves that the proposed method improves the recognition of difficult aerobics movements to achieve the goal of promoting the development level of aerobics and improving the public health of all people.