Exploring the synergistic effect of green low-carbon circular development in China is of typical significance for promoting a new chapter of environmental governance system and building a beautiful China. In this paper, the scientific significance of green low-carbon circular development is described, and an evaluation system for collaborative development of composite system is constructed. LSTM-BP neural network is used to predict the development path under different modes. The study found that in the past 20 years, all subsystems have realized the transformation from low level order to medium level order, among which social and resource subsystems have stepped into high level order stage. Since 2013, the composite system has been transformed into a mid-level coordination stage, which benefits from policy macro-control, social transformation and progress, high-quality economic development, energy optimization and adjustment, efficient utilization of resources and continuous improvement of the environment. In the future, under the guidance of carbon peak, the synergistic effect of subsystems will promote the high-quality development of composite system.