The dynamical attractor of the modified Chaplygin gas(MEG)model is studied.The dynamical analysis indicates that the phase ωMCG=-1 is a dynamical attractor and the equation of state of the MCG approaches it from either ωMMCG＞-1 or ωMCG＜-1,independent of the choice of its initial density parameter and the ratio of pressure to critical energy density.Therefore our universe will not end up with Big Rip in the future.Moreover,the evolutions of the density parameters Ωγand ΩMCG are quite different.For different initial values of x and y,Ωγ decreases and ΩMCG increases as time increases,and they will eventually approach Ωγ=0 and ΩMCG=1,i.e.,de Sitter phase.This implies that when there is not the interaction(i.e.,the energy transfer)between the barotropic background fluid and modified Chaplygin gas(MCG),the behaviour of the MCG will be similar to ACDM in the future.