Warehousing demand prediction is an essential part of the supply chain, providing a fundamental basis for product manufacturing, replenishment, warehouse planning, etc. Existing forecasting methods cannot produce accurate forecasts since warehouse demand is affected by external factors such as holidays and seasons. Some aspects, such as consumer psychology and producer reputation, are challenging to quantify. The data can fluctuate widely or do not show obvious trend cycles. We introduce a new model for warehouse demand prediction called MAGRU, which stands for Multi-layer Attention with GRU. In the model, firstly, we perform the embedding operation on the input sequence to quantify the external influences; after that, we implement an encoder using GRU and the attention mechanism. The hidden state of GRU captures essential time series. In the decoder, we use attention again to select the key hidden states among all-time slices as the data to be fed into the GRU network. Experimental results show that this model has higher accuracy than RNN, LSTM, GRU, Prophet, XGboost, and DARNN. Using mean absolute error (MAE) and symmetric mean absolute percentage error(SMAPE) to evaluate the experimental results, MAGRU's MAE, RMSE, and SMAPE decreased by 7.65%, 10.03%, and 8.87% over GRU-LSTM, the current best model for solving this type of problem.