In　this　paper,　we　mainly　investigate　the　optimization　model　that　minimizes　the　cost　function　such　that　the　cover　function　exceeds　a　required　threshold　in　the　set　cover　problem,　where　the　cost　function　is　additive　linear,　and　the　cover　function　is　non-monotone　approximately　submodular.　We　study　the　problem　under　streaming　model　and　propose　three　bicriteria　approximation　algorithms.　Firstly,　we　provide　an　intuitive　streaming　algorithm　under　the　assumption　of　known　optimal　objective　value.　The　intuitive　streaming　algorithm　returns　a　solution　such　that　its　cover　function　value　is　no　less　than　a　(1　-6)　times　threshold,　and　the　cost　function　is　no　more　than　(2　+　?　)(2)=(?　(2)?(2))　K,　where　K　is　a　value　that　we　suppose　for　the　optimal　solution　and　a　is　the　approximation　ratio　of　an　algorithm　for　unconstrained　maximization　problem　that　we　can　call　directly.　Next　we　present　a　bicriteria　streaming　algorithm　scanning　the　ground　set　multi-pass　to　weak　the　assumption　that　we　guess　the　optimal　objective　value　in　advance,　and　maintain　the　same　bicriteria　approximation　ratio.　Finally　we　modify　the　multi-pass　streaming　algorithm　to　a　single-pass　one　without　compromising　the　performance　ratio.　Additionally,　we　also　propose　some　numerical　experiments　to　test　our　algorithm＇s　performance　comparing　with　some　existing　methods.