According to the characteristics of continuous value prediction and the imitation of the sample data size of cold chain logistics demand, an improved BP neural network model based on gating mechanism and GELU is proposed. Through gating mechanism, neural network pays more attention to important features in input, and GELU is used as the activation function of neural network, which can provide better nonlinear ability. In the empirical process, the model is used to forecast the demand of cold chain logistics of agricultural products in Hubei Province. The improved BP neural network achieves 96.07% similarity on the test dataset, which represents the state of the art in cold chain logistics demand forecast.