We consider the large-time behavior of solutions to hyperbolic-parabolic coupled systems in the half line.Assuming that the systems admit the entropy function,we may rewrite them to symmetric forms.For the symmetrizable hyperbolic-parabolic systems,we first prove the existence of the stationary solution.We also prove that the stationary solution is time asymptotically stable under a smallness assumption on the initial perturbation.Moreover,we obtain the convergence rate towards the stationary solutions.These theorems for the general hyperbolic-parabolic system cover the compressible Navier-Stokes equation for heat conductive gas.