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In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod(1984) and J E Dunn and J Serrin(1985). We establish the existence, uniqueness and exponential stability of global solutions in H2 × H 1 × H 1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates, which implies the existence and exponential stability of the nonlinear C0-semigroups S(t) on H2 × H1 × H1.