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To improve the precision of carbon price forecasting, our study aims to propose a novel hybrid forecasting model which integrates recurrent neural networks and attention mechanisms. First, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm is employed to decompose carbon prices into several regular intrinsic mode functions (IMFs) and a residual. Second, multiscale entropy is utilized to differentiate and reconstruct these components to reduce cumulative errors in subsequent forecasting. Subsequently, a bidirectional long short-term memory network (Bi-LSTM) equipped with attention mechanisms is used to forecast each reconstructed component. Attention mechanisms identifies crucial sequence elements, assigns different weights to hidden information, and extracts richer information from the series. Finally, the results of all components are integrated to obtain the final forecasting result. Empirical analysis conducted on real datasets from the Guangdong and Hubei carbon markets demonstrates that the proposed hybrid model outperform prevailing mainstream forecasting models in terms of both horizontal and directional forecasting metrics. • A hybrid forecasting model is proposed for carbon price forecasting. • ICEEMDAN algorithm is employed to decompose carbon prices into several simple modes. • Bi-LSTM equipped with attention mechanisms is used to forecast each mode. • The proposed hybrid model outperform prevailing mainstream forecasting models. [ABSTRACT FROM AUTHOR]