In　this　paper,　an　adjustable　Q　-learning　scheme　is　developed　to　solve　the　discrete　-time　nonlinear　zero　-sum　game　problem,　which　can　accelerate　the　convergence　rate　of　the　iterative　Q　-function　sequence.　First,　the　monotonicity　and　convergence　of　the　iterative　Q　-function　sequence　are　analyzed　under　some　conditions.　Moreover,　by　employing　neural　networks,　the　model　-free　tracking　control　problem　can　be　overcome　for　zerosum　games.　Second,　two　practical　algorithms　are　designed　to　guarantee　the　convergence　with　accelerated　learning.　In　one　algorithm,　an　adjustable　acceleration　phase　is　added　to　the　iteration　process　of　Q　-learning,　which　can　be　adaptively　terminated　with　convergence　guarantee.　In　another　algorithm,　a　novel　acceleration　function　is　developed,　which　can　adjust　the　relaxation　factor　to　ensure　the　convergence.　Finally,　through　a　simulation　example　with　the　practical　physical　background,　the　fantastic　performance　of　the　developed　algorithm　is　demonstrated　with　neural　networks.