In　previous　studies　of　the　spatial　public　goods　game,　each　player　is　able　to　establish　a　group.　However,　in　real　life,　some　players　cannot　successfully　organize　groups　for　various　reasons.　In　this　paper,　we　propose　a　mechanism　of　reputation-driven　group　formation,　in　which　groups　can　only　be　organized　by　players　whose　reputation　reaches　or　exceeds　a　threshold.　We　define　a　player＇s　reputation　as　the　frequency　of　cooperation　in　the　last　T　time　steps.　We　find　that　the　highest　cooperation　level　can　be　obtained　when　groups　are　only　established　by　pure　cooperators　who　always　cooperate　in　the　last　T　time　steps.　Effects　of　the　memory　length　T　on　cooperation　are　also　studied.　©　2017　IOP　Publishing　Ltd　and　SISSA　Medialab　srl.