In　this　brief,　a　novel　accelerated　Q-learning　algorithm　is　developed　to　address　optimal　control　problems　for　discrete-time　nonlinear　systems.　First,　the　accelerated　Q-learning　scheme　is　proposed　by　introducing　the　relaxation　factor.　Note　that　the　relaxation　factor　leads　to　the　adjustability　of　the　convergence　rate.　Second,　the　convergence　of　the　Q-function　is　analyzed　with　different　relaxation　factors.　Third,　the　adjustable　Q-learning　scheme　is　developed　with　guaranteed　convergence,　which　can　adaptively　change　the　value　of　the　relaxation　factor.　Finally,　the　simulation　results　demonstrate　the　effectiveness　of　this　proposed　algorithm.