This　paper　investigates　a　new　stochastic　green　production　planning　problem　without　full　knowledge　about　the　probability　distribution　on　customer　demands.　The　only　information　regarding　the　demand　is　the　means　and　covariance　matrix.　The　goal　of　the　study　is　to　provide　an　eco-conscious　manufacturer　with　solution　methods　capable　of　yielding,　within　a　reasonable　amount　of　computation　time,　a　robust　solution　that　maximizes　customer　satisfaction　while　taking　into　account　the　constraints　of　budgets　and　periodic　carbon　caps　spontaneously　set　out　of　environmental　awareness.　We　formulate　the　problem　into　a　novel　distributionally　robust　chance-constrained　optimization　model　under　demand　uncertainty　set.　To　effectively　solve　the　model,　two　heuristics　are　proposed.　The　widely　used　sample　average　approximation　(SAA)　scheme　is　first　deployed　as　a　benchmark　method.　However,　the　computation　time　increases　rapidly　with　the　problem　size.　In　some　instances,　even　feasible　solutions　cannot　be　found　within　a　reasonable　amount　of　computation　time.　We　then　develop　an　approximated　mixed-integer　reformulation　on　the　basis　of　second　order　cone　program　(SOCP).　A　real-world　case　is　solved　and　extensive　numerical　experiments　show　that　the　SOCP　heuristic　is　superior　over　the　SAA　heuristic　in　terms　of　computation　time　while　the　solution　quality　is　only　slightly　lower　in　most　of　instances.　Finally,　sensitivity　analysis　on　budgets,　periodic　carbon　caps,　the　maximum　budget　overrun　risk　level,　initial　inventory　levels,　and　the　magnitude　of　demand　uncertainty　are　conducted　and　useful　managerial　insights　are　derived.