Global warming caused by increased carbon emissions is a common challenge for all mankind. Facing the unprecedented pressure of carbon emission reduction, it is particularly important to grasp the dynamics of carbon emission in time and accurately. This paper proposes a novel daily carbon emission forecasting model. Firstly, the daily carbon emission data is decomposed into a series of completely noise-free mode functions by improved complete ensemble empirical mode decomposition method with adaptive noise (ICEEMDAN). Then, a two-stage feature selection method composed of partial autocorrelation function (PACF) and ReliefF is applied to select appropriate input variables for the next prediction process. Finally, the extreme learning machine optimized by improved sparrow search algorithm (ISSA-ELM) is used to predict. The empirical results show that the proposed two-stage feature selection method can further improve the prediction accuracy. After two-stage feature selection, the values of R2, MAPE, and RMSE were improved by 0.55%, 30.23%, and 28.46%, respectively. It can also be found that ISSA has good optimization performance. By combining with ISSA, R2, MAPE, and RMSE improved by 7.60%, 31.97%, and 44.79%, respectively. Therefore, the proposed model can provide a valuable reference for the formulation of carbon emission reduction policies and future carbon emission prediction research.