This　paper　presents　a　new　method　for　group　decision-making　(GDM)　under　multi-granular　hesitant　information　based　on　the　data　envelopment　analysis　(DEA)　cross-efficiency　approach　with　regret　theory　(MGDM-RCE),　which　addresses　some　limitations　of　classic　DEA　for　hesitant　linguistic　information,　such　as　ignoring　decision-makers　(DMs)＇s　non-rational　behavior　and　the　use　of　single-granularity　scales.　The　proposed　MGDM-RCE　method,　on　the　foundation　of　cross-efficiency　and　regret　theory　with　multi-granular　hesitant　fuzzy　linguistic　term　sets　(HFLTSs),　allows　for　constructing　two　cross-efficiency　models　based　on　total　regret-rejoice　utility　values　to　determine　cross-efficiency　intervals　of　decision-making　units　(DMUs).　Additionally,　an　extended　stochastic　cross　-efficiency　technique　is　developed　for　obtaining　the　final　ranking　of　alternatives　in　the　correlative　GDM　problem.　The　performance　of　the　MGDM-RCE　method　is　shown　using　a　numerical　example　consisting　of　selecting　new　energy　sources　and　its　validity　and　superiority　are　analyzed　through　sensitivity　and　comparative　analysis.　The　sensitivity　analysis　revealed　that　variations　in　the　parameters　of　the　MGDM-RCE　method　do　not　significantly　affect　the　ranking　results.　Moreover,　compared　to　the　classic　methods　VIKOR　and　TOPSIS,　the　MGDM-RCE　method　exhibits　higher　stability　characteristics　in　addressing　the　GDM　problem.