In　this　paper,　we　investigate　the　nonlinear　stability　of　contact　waves　for　the　Cauchy　problem　to　the　compressible　Navier-Stokes　equations　for　a　reacting　mixture　in　one　dimension.　If　the　corresponding　Riemann　problem　for　the　compressible　Euler　system　admits　a　contact　discontinuity　solution,　it　is　shown　that　the　contact　wave　is　nonlinearly　stable,　while　the　strength　of　the　contact　discontinuity　and　the　initial　perturbation　are　suitably　small.　Especially,　we　obtain　the　convergence　rate　by　using　anti-derivative　methods　and　elaborated　energy　estimates.