This talk is concerned with the evolution for a compressible isothermal mixture of binary fluids. The flow of such fluid can be described by the well-known diffuse interface system of equations nonlinearly couples the Navier-Stokes and Cahn-Hilliard equations, called Navier-Stokes-Cahn-Hilliard system. Here we investigated the large time behavior of solutions to the initial value problems for this system in one dimension. When the initial data tends to a constant state as x tends to infinity, and the limit state for the concentration difference of the two components lies in convex region of the free energy density, we prove that the solution of this system converges to the certain constant state as time tend to infinity. We show that the location of the initial proportional to the concentration difference of the two components play a key role for the phase separation. The proof is given by energy method and a careful analysis.