In　the　stochastic　facility　location　problem,　there　are　two-stage　processes　for　the　decision.　A　set　of　facilities　may　be　opened　without　information　for　the　demand　of　clients　at　the　first　stage;　an　additional　set　of　facilities　may　further　be　opened　at　the　second　stage　where　the　scenario　of　the　clients　is　realized　according　to　some　given　distribution.　One　has　to　take　the　risk　into　consideration　and　make　decision　on　the　open　facilities　in　each　stage　and　each　scenario　such　that　the　total　expected　cost　of　the　opening　and　service　is　minimized.　In　this　paper,　we　consider　a　global　cardinality　constraint　in　this　model,　i.e.,　there　is　an　upper　bound　k　for　the　number　of　open　facilities　at　the　second　stage.　This　model　generalizes　both　stochastic　facility　location　and　the　k-median.　Our　main　result　is　a　provable　efficient　approximation　algorithm　with　a　performance　ratio　of　6　based　on　primal-dual　schema.　©　2021,　Springer　Nature　Switzerland　AG.