This　work　is　a　continuation　of　our　previous　work　[Z.-Q.　Shao,　Global　structure　instability　of　Riemann　solutions　for　general　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary,　J.　Math.　Anal.　Appl.　330　(1)　(2007)　511-540].　In　the　present　paper,　we　study　the　global　structure　stability　of　the　Riemann　solution　u　=　U(x/t),　containing　only　shocks　and　contact　discontinuities,　of　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　presence　of　a　boundary.　We　prove　the　existence　and　uniqueness　of　global　piecewise　C1　solution　containing　only　shocks　and　contact　discontinuities　to　a　class　of　the　mixed　initial-boundary-value-problem　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　the　half　space　{(t,　x)|t　≥　0,　x　≥　0}.　Our　result　indicates　that　this　kind　of　Riemann　solution　u　=　U(x/t)　mentioned　above　for　general　n　x　n　quasilinear　hyperbolic　systems　of　conservation　laws　in　a　half　space　possesses　a　global　structural　stability.　Some　applications　to　quasilinear　hyperbolic　systems　of　conservation　laws　arising　in　physics　and　other　disciplines　are　also　given.　©　2007　Elsevier　Ltd.　All　rights　reserved.