In　this　paper,　a　novel　value-iteration-based　adaptive　critic　scheme　is　developed　to　address　the　H-infinity　control　problem　for　non-linear　non-affine　continuous-time　(CT)　systems　with　disturbances.　Recurrent　neural　networks　are　employed　to　model　the　non-linear　non-affine　systems,　thereby　covering　the　unknown　system　dynamics.　Based　on　the　transformation　of　the　optimal-robust　problem,　the　H-infinity　control　issue　is　established　to　deal　with　disturbances.　By　introducing　the　accelerated　factor,　the　value-iteration-based　adaptive　dynamic　programming　approach　is　developed　to　design　controllers　for　non-linear　CT　systems　subject　to　input　constraints.　The　initial　admissible　control　law　is　eliminated,　which　is　a　tough　question　for　traditional　policy　iteration.　Besides,　the　speed　of　the　learning　process　is　improved　by　relying　on　the　accelerated　factor.　The　corresponding　convergence　of　the　established　method　and　the　stability　of　the　closed-loop　system　are　presented　by　giving　corresponding　theorems.　Finally,　the　effectiveness　of　novel　value-iteration-based　adaptive　critic　is　validated　by　conducting　two　examples.