Global carbon dioxide emissions have become a great threat to economic sustainability and human health. The carbon market is recognized as the most promising mean to curb carbon emissions, furthermore, carbon price forecasting will promote the role of the carbon market in emissions reduction and achieve reduction targets at lower economic costs for emission entities. However, there are still some technical problems in carbon price prediction, such as mode mixing and larger reconstruction error for the traditional empirical mode decomposition-type models. Therefore, the innovation of this paper is constructing a novel carbon price prediction model of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-long short-term memory (LSTM), that combines the advantages of CEEMDAN in decomposing the multiscale time-frequency carbon price signals and the LSTM model in fitting the financial signals. The results show the proposed CEEMDAN-LSTM model has significant accuracy in predicting the complex carbon price signals. The prediction error and expectation indicators of root mean square error, mean absolute error, mean absolute percentage error, and direction accuracy are 0.638342, 0.448695, 0.015666, and 0.687631, respectively, which is better than other benchmark models. Further evidence convince that the short-term forecasting performance is superior to the long-term and medium-term performance. That evidence concludes that the proposed model is a reliable method to reveal the carbon price-driving mechanism from the point of multiscale time-frequency characteristics. Particularly, short-term forecasting is more accurate and can provide a valuable technical reference for reduction entities and green financial companies to judge the market situation and formulate quantitative transactions.