In　this　paper,　a　novel　value　iteration　adaptive　dynamic　programming　(ADP)　algorithm　is　presented,　which　is　called　an　improved　value　iteration　ADP　algorithm,　to　obtain　the　optimal　policy　for　discrete　stochastic　processes.　In　the　improved　value　iteration　ADP　algorithm,　for　the　first　time　we　propose　a　new　criteria　to　verify　whether　the　obtained　policy　is　stable　or　not　for　stochastic　processes.　By　analyzing　the　convergence　properties　of　the　proposed　algorithm,　it　is　shown　that　the　iterative　value　functions　can　converge　to　the　optimum.　In　addition,　our　algorithm　allows　the　initial　value　function　to　be　an　arbitrary　positive　semi-definite　function.　Finally,　two　simulation　examples　are　presented　to　validate　the　effectiveness　of　the　developed　method.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.