The　new　concepts　of　the　Z-C-X　space　and　excellent　cone　are　introduced.　Some　problems　of　random　semiclosed　1-set-contractive　operator　are　investigated　in　the　Z-C-X　space.　At　first,　an　important　inequality　is　proved.　Secondly,　several　new　conclusions　are　proved　by　means　of　random　fixed　point　index　in　the　theory　of　random　topological　degree.　A　random　solution　of　a　class　of　random　operator　equations　under　conditions　of　imitating　the　parallelogram　law　is　obtained,　famous　Altman＇s　theorem　is　generalized　in　partially　ordered　Z-C-X　space.　Therefore,　some　new　results　are　obtained.