Short-term power load forecasting is of great significance for the reliable and safe operation of power systems. In order to improve the accuracy of short-term load forecasting, for the problems of random fluctuation in load and the complexity of load-influencing factors, this paper proposes a two-stage short-term load forecasting method, SSA–VMD-LSTM-MLR-FE (SVLM–FE) based on sparrow search algorithm (SSA), to optimize variational mode decomposition (VMD) and feature engineering (FE). Firstly, an evaluation criterion on the loss of VMD decomposition is proposed, and SSA is used to find the optimal combination of parameters for VMD under this criterion. Secondly, the first stage of forecasting is carried out, and the different components obtained from SSA–VMD are predicted separately, with the high-frequency components input to a long short-term memory network (LSTM) for forecasting and the low-frequency components input to a multiple linear regression model (MLR) for forecasting. Finally, the forecasting values of the components obtained in the first stage are input to the second stage for error correction; factors with a high degree of influence on the load are selected using the Pearson correlation coefficient (PCC) and maximal information coefficient (MIC), and the load value at the moment that has a great influence on the load value at the time to be predicted is selected using autocorrelation function (ACF). The forecasting values of the components are fused with the selected feature values to construct a vector, which is fed into the fully connected layer for forecasting. In this paper, the performance of SVLM–FE is evaluated experimentally on two datasets from two places in China. In Place 1, the RMSE, MAE, and MAPE are 128.169 MW, 102.525 MW, and 1.562%, respectively; in Place 2, the RMSE, MAE, and MAPE are 111.636 MW, 92.291 MW, and 1.426%, respectively. The experimental results show that SVLM–FE has high accuracy and stability.