In　this　paper,　we　introduce　a　model　of　distributionally　robust　facility　location　problem　(DRFLP)　under　moment　constraints　up　to　the　second　order.　We　show,　via　duality　theory　of　moment　problems,　that　the　linear　relaxation　of　the　DRFLP　is　equivalent　to　that　of　the　standard　uncapacitated　facility　location　problem　(UFLP).　Consequently,　any　LP-based　approximation　algorithm　for　the　UFLP　implies　an　approximation　algorithm　for　the　DRFLP　with　the　same　approximation　ratio.