This　research　investigates　the　bidirectional　cointegration　relationship　between　environmental,　social,　and　governance　(ESG)　performance　and　corporate　green　innovation　with　a　panel　of　770　Chinese　listed　firms　during　the　2011-2020.　We　find　that　there　exists　a　long-run　bidirectional　comovement　between　ESG　performance　and　corporate　green　innovation　output.　ESG　performance　exerts　a　short-run　and　long-run　causal　link　with　green　innovation　output.　The　panel　cointegration　test　and　VECM　estimation　also　support　that　ESG　performance　moves　together　with　green　innovation　output　for　clean　industries,　while　ESG　performance　only　presents　a　long-run　relationship　to　green　invention　patents　output　for　pollution　industries.　Our　findings　offer　important　value　for　policymakers　and　enterprises　to　propose　an　effective　strategy　to　stimulate　green　innovation　and　improve　ESG　score.