It is significant to study the risk spillover effect and reveal the internal mechanism and rule between China’s carbon market and seven stock sector markets of Power, Material, Real Estate, Industrial, Finance, Traditional Energy and New Energy to prevent carbon financial risks effectively. According to the generalized forecast error variance decomposition model and the complex network method, a spillover model was constructed to capture the static and time-varying spillover effect, and a connectedness network was founded to identify the centre and evolution of risk. The results indicated that China’s carbon market is a net receiver of risk from stock sector markets. The characteristics of the spillover effects and the net spillover relationships between China’s carbon market and diverse stock sector markets had differences. Among them, the new energy market has the most significant spillover effect on the carbon market. In addition, policy changes and macroeconomic shocks can impact the time-varying spillover. The industrial market is the centre of the connectedness network. Based on these conclusions, some policy suggestions are put forward.