In　practical　industrial　processes,　the　receding　optimization　solution　of　nonlinear　model　predictive　control　(NMPC)　is　always　a　very　knotty　problem.　Based　on　adaptive　dynamic　programming,　the　accelerated　value　iteration　predictive　control　(AVI-PC)　algorithm　is　developed　in　this　paper.　Integrating　iteration　learning　with　the　receding　horizon　mechanism　of　NMPC,　a　novel　receding　optimization　solution　pattern　is　exploited　to　resolve　the　optimal　control　law　in　each　prediction　horizon.　Besides,　the　basic　architecture　and　the　specific　form　of　the　AVI-PC　algorithm　are　demonstrated,　including　the　relationship　among　the　iterative　learning　process,　the　prediction　process,　and　the　control　process.　On　this　basis,　the　convergence　and　admissibility　conditions　are　established,　and　the　relevant　properties　are　comprehensively　analyzed　when　the　accelerated　factor　satisfies　the　established　conditions.　Furthermore,　the　accelerated　value　iterative　function　is　approximated　through　the　single　critic　network　constructed　by　utilizing　the　multiple　linear　regression　method.　Finally,　the　plentiful　simulation　experiments　are　conducted　from　various　perspectives　to　verify　the　effectiveness　and　progressiveness　of　the　AVI-PC　algorithm.　©　2024　Elsevier　Ltd