To　investigate　the　effect　of　disturbance　on　nonlinear　control,　we　employ　an　adaptive　critic　control　algorithm　to　solve　the　zero-sum　game　problems　for　discrete-time　nonlinear　systems.　Multi-step　adaptive　critic　control　(MsACC)　design　is　considered　by　combining　the　heuristic　dynamic　programming　algorithm　and　multi-step　policy　evaluation.　Using　multi-step　system　information,　the　optimal　control　strategy　can　be　found　faster　than　traditional　methods.　In　addition,　we　analyze　the　stability　of　the　MsACC　algorithm.　In　order　to　realize　the　MsACC　algorithm,　three　neural　networks　are　established　to　approximate　the　control　input,　the　disturbance　input,　and　the　cost　function,　respectively.　Finally,　a　simulation　example　verifies　that　the　proposed　scheme　can　efficiently　solve　the　zero-sum　game　problem　for　nonlinear　systems.　©　2023　IEEE.