This　article　puts　emphasis　on　the　deterministic　value-iteration-based　Q-learning　(VIQL)　algorithm　with　adjustable　convergence　speed,　followed　by　the　application　verification　on　trajectory　tracking　for　completely　unknown　nonaffine　systems.　It　is　worth　emphasizing　that,　under　the　effect　of　learning　rates,　the　convergence　speed　can　be　adjusted　and　the　new　convergence　criterion　of　the　VIQL　framework　is　investigated.　The　merit　of　the　adjustable　VIQL　scheme　is　that　it　can　quicken　the　learning　speed　and　decrease　the　number　of　iterations,　thereby　reducing　the　computation　burden.　To　carry　out　the　model-free　VIQL　algorithm,　the　offline　data　of　system　states　and　reference　trajectories　are　collected　to　provide　the　reference　control,　the　tracking　error,　and　the　tracking　control,　which　promotes　the　parameter　updating　of　the　adjustable　VIQL　algorithm　via　the　off-policy　learning　scheme.　By　this　updating　operation,　the　convergent　optimal　tracking　policy　can　guarantee　that　arbitrary　initial　state　tracks　the　desired　trajectory　and　can　completely　obviate　the　terminal　tracking　error.　Finally,　numerical　simulations　are　conducted　to　indicate　the　validity　of　the　designed　tracking　control　algorithm.