In　this　paper,　an　adaptive　critic　control　method　based　on　the　neural　networks　is　established　for　multi-player　non-zero-sum　games　with　asymmetric　constraints　of　continuous-time　nonlinear　systems.　First,　a　novel　nonquadratic　function　is　proposed　to　deal　with　asymmetric　constraints,　and　then　the　optimal　control　laws　and　the　coupled　Hamilton-Jacobi　equations　are　derived.　It　is　worth　noting　that　the　optimal　control　strategies　do　not　stay　at　zero　when　the　system　state　is　zero,　which　is　different　from　the　past.　After　that,　only　a　critic　network　is　constructed　to　approximate　the　optimal　cost　function　for　each　player,　so　as　to　obtain　the　associated　approximate　optimal　control　strategies.　Meanwhile,　a　new　weight　updating　rule　is　developed　during　critic　learning.　In　addition,　the　stability　of　the　weight　estimation　errors　of　critic　networks　and　the　closed-loop　system　state　is　proved　by　utilizing　the　Lyapunov　method.　Finally,　simulation　results　verify　the　effectiveness　of　the　method　proposed　in　this　paper.　©　2023　South　China　University　of　Technology.　All　rights　reserved.