We　consider　weak　solutions　to　a　simplified　Ericksen-Leslie　system　of　two-dimensional　compressible　flow　of　nematic　liquid　crystals.　An　initial-boundary　value　problem　is　first　studied　in　a　bounded　domain.　By　developing　new　techniques　and　estimates　to　overcome　the　difficulties　induced　by　the　supercritical　nonlinearity　in　the　equations　of　angular　momentum　on　the　direction　field,　and　adapting　the　standard　three-level　approximation　scheme　and　the　weak　convergence　arguments　for　the　compressible　Navier-Stokes　equations,　we　establish　the　global　existence　of　weak　solutions　under　a　restriction　imposed　on　the　initial　energy　including　the　case　of　small　initial　energy.　Then　the　Cauchy　problem　with　large　initial　data　is　investigated,　and　we　prove　the　global　existence　of　large　weak　solutions　by　using　the　domain　expansion　technique　and　the　rigidity　theorem,　provided　that　the　second　component　of　initial　data　of　the　direction　field　satisfies　some　geometric　angle　condition.