Accurate short-term load forecasting (STLF) plays an essential role in sustainable energy development. Specifically, energy companies can efficiently plan and manage their generation capacity, lessening resource wastage and promoting the overall efficiency of power resource utilization. However, existing models cannot accurately capture the nonlinear features of electricity data, leading to a decline in the forecasting performance. To relieve this issue, this paper designs an innovative load forecasting method, named Prophet–CEEMDAN–ARBiLSTM, which consists of Prophet, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and the residual Bidirectional Long Short-Term Memory (BiLSTM) network. Specifically, this paper firstly employs the Prophet method to learn cyclic and trend features from input data, aiming to discern the influence of these features on the short-term electricity load. Then, the paper adopts CEEMDAN to decompose the residual series and yield components with distinct modalities. In the end, this paper designs the advanced residual BiLSTM (ARBiLSTM) block as the input of the above extracted features to obtain the forecasting results. By conducting multiple experiments on the New England public dataset, it demonstrates that the Prophet–CEEMDAN–ARBiLSTM method can achieve better performance compared with the existing Prophet-based ones.