Based on the main livestock products prices from June 1994 to August 2016 including pork,beef and lamb through a sequence of self correlation function diagram and Hurst value,this paper uses R/S rescaled range method to measure the long memory of animal products prices.At the same time,the model of AFRIMA and ARIMA was established in order to compare the prediction accuracy after calculating fractional differential order.The result shows that the price of animal products has long memory and slow sequence decay process,the accuracy of AFRIMA prediction is high,pork price volatility is predicted to fall in the state of low speed fluctuations,beef prices show gradually reduced volatility and rising weakness.Lamb prices are expected to decline and the price is in a stalemate recently.Therefore,this paper proposes that long term memory should be fully considered in the research and forecast of fluctuation of livestock product prices.The relevant departments should consider the long memory characteristics of the price and pay more attention to the correlation of pre price volatility and future price fluctuation in the formulation of relevant macro control policies.