To meet carbon peak and neutrality targets, accurate carbon trading price forecasting is very important for enterprises making emission reduction decisions. By fusing convolutional neural network (CNN) and long short-term memory network (LSTM), the CNN–LSTM model is constructed. After variational mode decomposition (VMD), several intrinsic mode functions (IMFs) components are obtained and input into the CNN–LSTM model, thus constructing the combined sooty tern optimization algorithm (STOA)–VMD–CNN–LSTM forecasting model. To test this model, the carbon trading prices of the carbon emission trading markets of Hubei, Guangdong and Shenzhen were forecast. The prediction performance of the STOA–VMD–CNN–LSTM model is compared with ARIMA, BP, CNN and LSTM benchmark models and models combining different decomposition technologies. The international carbon trading price (EUR and CER) is used for prediction. Compared with other methods, the developed model makes fewer errors and achieves superior performance. Several important implications are provided for investors and risk managers involved in carbon financial products. [ABSTRACT FROM AUTHOR]