A　new　system　of　generalized　set-valued　mixed　equilibrium-like　problems　(in　short,　S-GMELP)　in　Banach　spaces　is　discussed.　In　order　to　obtain　the　existence　of　solutions　of　S-GMELP,　a　system　of　related　auxiliary　problems　(in　short,　S-AP)　is　established.　On　the　basis　of　the　existence　and　uniqueness　of　solutions　of　the　S-AP,　an　iterative　algorithm　for　the　S-GMELP　is　constructed.　It　is　proved　that　the　iterative　sequence　converges　some　solution　of　S-GMELP.　Finally,　an　example　is　given　to　well　exemplify　our　main　result.