In　this　paper,　a　novel　optimal　control　scheme　is　established　to　solve　the　multi-player　zero-sum　game　(ZSG)　issue　of　continuous-time　nonlinear　systems　with　control　constraints　and　unknown　dynamics　based　on　the　adaptive　critic　technology.　To　relax　the　requirement　of　system　dynamics,　a　neural　network-based　identifier　is　applied　to　reconstruct　the　unknown　multi-player　ZSG　system.　Then,　by　developing　a　new　nonquadratic　function,　the　associated　Hamilton-Jacobi-Isaacs　(HJI)　equation　of　the　constrained　ZSG　is　derived.　Moreover,　an　adaptive　critic　framework　is　constructed　to　approximate　the　optimal　cost　function.　Meanwhile,　the　strategy　sets　of　optimal　control　and　the　worst　disturbance　are　estimated　by　utilizing　the　single-critic　network,　respectively.　After　that,　a　modified　critic　weight　updating　mechanism　with　experience　replay　technique　is　introduced　to　relax　the　requirement　of　the　persistence　of　excitation　condition.　Theoretically,　by　employing　the　Lyapunov　stability　theorem,　the　uniform　ultimate　boundedness　stability　of　the　ZSG　system　state　and　the　critic　network　weight　approximation　error　are　proved.　Finally,　a　representative　example　is　simulated　to　validate　the　efficacy　of　the　constructed　framework.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.