The sudden eruption of COVID-19 has inflicted tremendous damage to the worldwide economy, and stock markets have become violently volatile due to its negative impact. Therefore, accurate forecasting of stock price index has been playing an essential role in maintaining national economic security and formulating related policies. In this paper, a novel decomposition-ensemble model is proposed to predict the highly fluctuating stock price index. To begin with, the modified ensemble empirical mode decomposition (MEEMD) method is adopted to decompose the original stock price index into subsequences with different frequencies. Then, the last high-frequency subsequence and other subsequences are predicted through multilayer perceptron (MLP) and long short-term memory (LSTM), respectively. Finally, the prediction outcomes of different model subsequences are reconstructed into the ultimate prediction results by utilizing the integration method. Compared with the contrast models, the MEEMD-LSTM-MLP model proposed in our paper not only demonstrates significant advantages in multi-step forecasting for both emerging and developed markets, but also achieves excellent prediction performance amidst the severe market fluctuations triggered by COVID-19. Furthermore, the application of the MEEMD-LSTM-MLP model is extended to financial time series with different data characteristics and market types, which further proves its high applicability and reliability. Therefore, the conducted hybrid MEEMD-LSTM-MLP model is an effective and stable multi-step forecasting tool to provide valuable intelligent technical support for governments and enterprises in complex economic conditions.