The promotion of carbon market can accelerate the pace of low-carbon transformation of China's economic structure and achieve more efficient carbon emission reduction. Accurate carbon price prediction is conducive to improving the risk management of carbon market and the decision-making of investors, but it also brings great challenges to relevant industry practitioners and the government. In this paper, a new hybrid model is proposed, which combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and genetic algorithm (GA) optimized extreme learning machine (ELM). The application of GA-ELM in carbon price prediction is firstly studied in this paper. Eight intrinsic mode functions and one residual can be obtained by CEEMDAN, and then partial autocorrelation (PACF) is used to determine the partial correlation between each sequence and its lag data, and they were taken as internal factors affecting the prediction. At the same time, energy, economic and social factors are selected as the external factors affecting the prediction, and the carbon price prediction is realized through internal and external factors. It has been proved that the model successfully overcomes the challenge of carbon price prediction based on multiple influencing factors. The hybrid model shows superiority in Beijing, Shanghai and Guangdong. The results show that the prediction performance of the proposed model is the best among the 15 models, and the prediction accuracy will be improved due to the decomposition of the carbon price. Besides, the CEEMDAN-GA-ELM model better overcomes the challenge of carbon price prediction with multiple influencing factors. This model provides a novel and effective tool for the government and enterprises to predict the carbon price.