Carbon price fluctuation is affected by both internal market mechanisms and the heterogeneous environment. Moreover, it is a complex dynamic evolution process. This paper focuses on carbon price fluctuation trend prediction. In order to promote the accuracy of the forecasting model, this paper proposes the idea of integrating network topology information into carbon price data; that is, carbon price data are mapped into a complex network through a visibility graph algorithm, and the network topology information is extracted. The extracted network topology structure information is used to reconstruct the data, which are used to train the model parameters, thus improving the prediction accuracy of the model. Five prediction models are selected as the benchmark model, and the price data of the EU and seven pilot carbon markets in China from June 19, 2014, to October 9, 2020, are chosen as the sample for empirical analysis. The research finds that the integration of network topology information can significantly improve the price trend prediction of the five benchmark models for the EU carbon market. However, there are great differences in the accuracy improvement effects of China’s seven pilot carbon market price forecasts. Moreover, the forecasting accuracy of the four carbon markets (i.e., Guangdong, Chongqing, Tianjin, and Shenzhen) has improved slightly, but the prediction accuracy of the carbon price trend in Beijing, Shanghai, and Hubei has not improved. We analyze the reasons leading to this result and offer suggestions to improve China’s pilot carbon market.