A　multi-period　Stackelberg　game　is　adopted　to　study　a　green　procurement　relationship　between　manufacturers　and　suppliers　in　a　supply　chain.　The　manufacturers　are　considered　as　leaders,　while　the　suppliers　are　modelled　as　followers　in　this　Stackelberg　game.　Accordingly,　a　mixed　binary　linear　bi-level　programming　model　is　developed　to　elaborate　the　game　in　consideration　of　carbon　tax　scheme.　The　upper　level　(the　leader)　aims　at　selecting　a　proper　number　of　suitable　suppliers　to　provide　heterogeneous　raw　materials　at　the　lowest　operational　cost.　The　objective　of　the　lower　level　(the　follower)　is　to　find　optimal　purchasing　quantities　of　raw　materials.　In　addition,　two　lemmas　are　introduced　to　transform　the　mixed　linear　bi-level　programming　model　into　a　single　level　linear　programming　model.　The　numerical　example　illustrates　that:　(1)　the　manufacturer　prefers　to　adopt　the　multiple　sourcing　strategy　due　to　the　flexibility;　(2)　keeping　stable　supplies　and　large　order　volumes　could　effectively　reduce　carbon　emissions　for　the　suppliers　and　make　the　supply　chain　greener.　©　2018　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.