The work aims to compare and study the errors of different prediction methods to select a more accurate method for predicting the logistics demand of fresh agricultural products, and provide a reference for scientific and rational decision-making in the fresh agricultural product market in Shandong Province under the epidemic situation. With ten influencing factors, such as highway cargo turnover, Internet penetration rate, GDP, population, and added value of the primary industry, as independent variables, and the demand for fresh agricultural products as the dependent variable, the data prediction of five methods such as wavelet neural network, BP neural network, BP neural network by genetic algorithm (GA-BP), BP neural network by particle swarm (PSO-BP), long short-term memory (LSTM)were compared and analyzed. The predicted values of wavelet neural network and BP neural network were obviously lower than the actual values, and the average relative error was close to 20%, while the errors of optimized GA−BP, PSO−BP and LSTM algorithms were all less than 5%, which were 4.06%, 1.162% and 0.45% respectively. Therefore, LSTM had the highest prediction accuracy and the best effect. In the future, the demand for fresh agricultural products in Shandong Province will continue to grow, and the LSTM algorithm will be more applied in the field of logistics research due to its advantages of higher accuracy and stronger learning ability.