The　continuous-time　zero-sum　game　problem　with　asymmetric　constraints　is　investigated　by　making　use　of　the　adaptive　critic　control　approach.　Firstly,　a　novel　nonquadratic　function　is　established　to　deal　with　the　asymmetric　constraint　problem,　which　relaxes　the　restriction　on　the　control　matrix.　Secondly,　the　optimal　control,　the　worst　disturbance,　and　the　Hamilton-Jacobi-Isaacs　equation　are　derived.　After　that,　an　adaptive　critic　control　method　is　constructed　to　approximate　the　optimal　cost　function,　so　as　to　obtain　the　near-optimal　control　as　well　as　the　near-worst　disturbance.　It　is　worth　mentioning　that　for　the　zero-sum　game　problem　with　asymmetric　constraints,　this　paper　proposes　an　innovative　critic　learning　criterion　to　strengthen　the　learning　process　and　eliminate　the　dependence　on　the　initial　admissible　control,　which　has　not　been　considered　in　previous　papers.　Moreover,　the　stability　of　the　system　state　and　the　weight　estimation　error　of　the　critic　network　is　proved　using　the　Lyapunov　method.　Finally,　the　effectiveness　of　the　proposed　algorithm　is　verified　by　utilizing　two　examples,　namely,　the　F-16　aircraft　and　the　inverted　pendulum.　At　the　same　time,　for　comparison,　the　simulation　results　under　the　traditional　learning　algorithm　are　provided　to　further　illustrate　the　feasibility　of　the　innovative　learning　criterion　proposed.　©　2025　Northeast　University.　All　rights　reserved.