We　continue　to　study　the　large　time　behavior　of　the　solution　to　a　gas-solid　free　boundary　problem　for　a　one-dimensional　model　system　of　compressible　viscous　gas　proposed　by　us　in　[SIAM　J.　Math.　Anal.,　34　(2003),　pp.　1331-1355],　where　the　travelling　wave　and　the　rarefaction　wave　were　investigated.　In　this　paper　we　prove　the　asymptotic　stability　of　the　superposition　of　a　travelling　wave　and　a　viscous　shock　wave　under　some　smallness　conditions.　The　asymptotic　behavior　of　the　free　boundary　is　also　obtained.　The　proof　is　given　by　the　elementary　energy　estimate.