The　adaptive　learning　and　prediction　of　a　highly　nonlinear　and　time-varying　bioreactor　benchmark　process　is　studied　using　NeurOn-Line,　a　graphical　tool　kit　for　developing　and　deploying　neural　networks　in　the　G2　real　time　intelligent　environment,　and　a　new　modified　Broyden,　Fletcher,　Goldfarb,　and　Shanno　(BFGS)　quasi-Newton　algorithm.　The　modified　BFGS　algorithm　for　the　adaptive　learning　of　back　propagation　(BP)　neural　networks　is　developed　and　embedded　into　NeurOn-Line　by　introducing　a　new　search　method　of　learning　rate　to　the　full　memory　BFGS　algorithm.　Simulation　results　show　that　the　adaptive　learning　and　prediction　neural　network　system　can　quickly　track　the　time-varying　and　nonlinear　behavior　of　the　bioreactor.