Short-term logistics demand forecasting is one of critical components of the smart logistics system. As short-term logistics demand data is non-stationary, nonlinear series with strong randomness and singular points, it is difficult to accurately predict short-term logistics demand. Therefore, this paper proposes EEMD-LMD-LSTM-LEC deep learning model for short-term logistics demand forecasting, based on ensemble empirical mode decomposition(EEMD), local mean decomposition(LMD), and long and short-term memory(LSTM) neural networks while considering local error correction(LEC). The proposed model is divided into two stages. In the first stage, the EEMD-LMD-LSTM model is constructed based on feature decomposition and feature extraction, to reduce the error caused by non-linearity, non-stationarity and randomness of short-term logistics demand. In the second stage, a local error correction model is constructed to adjust the prediction results in the first stage for reducing the error caused by the singular points of short-term logistics demand. The results show that the proposed EEMD-LMD-LSTM-LEC model works better than other eleven models, in terms of root mean square errors, mean absolute errors, mean absolute percentage errors and the adjusted coefficient of determination, including the mathematical statistics model---ARIMA, shallow machine learning models---support vector regression and the BP neural network, deep learning models---LSTM and the convolutional neural network, combined models---the deep belief network-LSTM, empirical mode decomposition(EMD)-LSTM, EEMD-LSTM, LMD-LSTM, EMD-LMD-LSTM and EEMD-LMD-LSTM.