The　escalating　air　pollution　resulting　from　traffic　congestion　has　necessitated　a　shift　in　traffic　control　strategies　towards　green　and　low-carbon　objectives.　In　this　study,　a　graph　convolutional　network　and　self-attention　value　decomposition-based　multi-agent　actor-critic　(GSAVD-MAC)　approach　is　proposed　to　cooperative　control　traffic　network　flow,　where　vehicle　carbon　emission　and　traffic　efficiency　are　considered　as　reward　functions　to　minimize　carbon　emissions　and　traffic　congestions.　In　this　method,　we　design　a　local　coordination　mechanism　based　on　graph　convolutional　network　to　guide　the　multi-agent　decision-making　process　by　extracting　spatial　topology　and　traffic　flow　characteristics　between　adjacent　intersections.　This　enables　distributed　agents　to　make　low-carbon　decisions　which　not　only　account　for　their　own　interactions　with　the　environment　but　also　consider　local　cooperation　with　neighboring　agents.　Further,　we　design　a　global　coordination　mechanism　based　on　self-attention　value　decomposition　to　guide　multi-agent　learning　process　by　assigning　various　weights　to　distributed　agents　with　respect　to　their　contribution　degrees.　This　enables　distributed　agents　to　learn　a　globally　optimal　low-carbon　control　strategy　in　a　cooperative　and　adaptive　manner.　In　addition,　we　design　a　cloud　computing-based　parallel　optimization　algorithm　for　the　GSAVD-MAC　model　to　reduce　calculation　time　costs.　Simulation　experiments　based　on　real　road　networks　have　verified　the　advantages　of　the　proposed　method　in　terms　of　computational　efficiency　and　control　performance.