Carbon price forecasting is helpful to the management of carbon markets and the formulation of enterprises’ carbon trading strategies. Most of the relevant literature uses forecasting models that can only capture unidirectional time series features, and it does not explain much about the reasons for changes in carbon price trends. This paper proposes a hybrid carbon price forecasting model and takes the daily closing price of carbon allowances in the Hubei carbon market as the research object. Firstly, the minimum absolute contraction and selection operator algorithm is used to screen the main factors influencing carbon prices. Secondly, the original carbon price series is decomposed by the variational mode decomposition model and reconstructed according to the sample entropy. Then, combined with the main influencing factors, the reconstructed series are forecasted separately by the bidirectional gated recurrent unit model, and the final forecasting value is obtained by integrating their forecasting results. Finally, the reasons for trend changes in forecasting results are explained based on the market environment and influencing factors. The result of the study shows that the hybrid model consisting of the variational mode decomposition model and the bidirectional gated recurrent unit model has advantages in forecasting accuracy, goodness of fit, and precision of forecasting direction. In addition, it indicates that the carbon price continued to rise in the early and middle phases due to the national carbon market, market speculation, and policy inducements. It declined and stabilized in the late phase due to the balance of supply and demand and the off-season for compliance. Without significant changes in the policy environment, it will continue to be in the price range of 45-50 yuan in the coming compliance cycle.