To　attenuate　the　effect　of　disturbances　on　control　performance,　a　multi-step　adaptive　critic　control　(MsACC)　framework　is　developed　to　solve　zero-sum　games　for　discrete-time　nonlinear　systems.　The　MsACC　algorithm　utilizes　multi-step　policy　evaluation　to　obtain　the　solution　of　the　Hamilton-Jacobi-Isaac　equation,　which　is　faster　than　that　of　the　one-step　policy　evaluation.　The　convergence　rate　of　the　MsACC　algorithm　is　adjustable　by　varying　the　step　size　of　the　policy　evaluation.　In　addition,　the　stability　and　convergence　of　the　MsACC　algorithm　are　proved　under　certain　conditions.　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,　the　effectiveness　of　the　MsACC　algorithm　is　verified　by　two　simulation　examples,　including　a　linear　system　and　a　nonlinear　plant.