With the increasing environmental and climate problems caused by global warming, more and more countries are paying attention to reducing carbon emissions. Accurately predicting carbon prices can help create a stable carbon market and mitigate global warming. Therefore, a combined model which has four modules is proposed, they are the decomposition of carbon price series, reorganization of subsequences, point forecasting, and interval forecasting. For data preprocessing of decomposition, it can reduce the non-linearity of sequences. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the original series into multiple Intrinsic Mode Functions (IMFs). Reorganization uses SampEn (SE) and T-test to reorganize the decomposed sequence into three new sequences according to actual meanings. For point prediction, the combined prediction model uses Particle Swarm Optimization (PSO) to obtain the optimal weights of Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU), which can integrate their strengths to improve prediction accuracy. Interval prediction is based on fitting the optimal distribution function by Maximum Likelihood Estimate (MLE). Different significance intervals can be obtained from the point prediction results and the distribution function. Empirical and comparative experiments show this combined model has excellent point and interval predictions. Besides, the significance and stability are demonstrated. Finally, some valuable references are provided for policymakers.