The beef and mutton price have stayed in a high level for a long time,which has showed the same trend.Studying the inner change rule between them is of great significance.Based on the quarterly data of beef and mutton price from 1995 to 2014,this paper uses LSTR model to empirically analyze their relationships.The results showed that: firstly,beef and mutton price are interacted with each other by consumption effect and production effect with nonlinear characteristics.In particular,the amplitude threshold value of beef and mutton price were 0.061 2 and 0.032 5 respectively and when the price moved above the threshold value,the price interaction would show nonlinear characteristics.Secondly,beef price had a greater influence on mutton price under the linear system and mutton price had a greater influence on beef price under the nonlinear system,which was different with results of VAR model.Thirdly,two stages should be divided according to the interaction between beef and mutton price,which was the first stage of linear characteristic from 1996 to the end of 2006,and the second stage of nonlinear characteristics since 2007.According to the threshold values and different interaction systems between the beef and mutton price, controlling measures covering the two markets should be taken.