Deep　belief　networks　(DBNs)　are　effective　deep　learning　models　and　widely　used　to　analyze　big　data　characteristics,　extract　features,　and　approximate　nonlinear　systems.　However,　due　to　their　deep　structure　and　numerous　parameters,　DBNs　suffer　from　a　time-consuming　training　process　generally.　To　address　this　problem　and　improve　the　training　efficiency　without　reducing　accuracy,　this　article　proposes　a　self-optimizing　DBN　with　adaptive-active　learning　(SODBN-AAL).　In　the　proposed　SODBN-AAL,　an　adaptive　learning　algorithm　of　hyperparameters　is　designed　to　ensure　a　good　accuracy.　On　this　basis,　an　active　learning　algorithm　is　developed　based　on　an　event-triggered　strategy　to　improve　training　efficiency　by　extracting　effective　data　and　skipping　invalid　ones.　As　a　self-optimizing　model,　SODBN-AAL　combines　the　advantages　of　both　adaptive　hyperparameters　the　event-triggered　active　learning　(ETAL).　The　convergence　analysis　of　SODBN-AAL　is　presented　as　well.　Two　simulation　experiments　on　2D　function　approximation　and　water　quality　prediction　are　conducted　to　show　the　advantages　of　SODBN-AAL.　The　results　show　that,　compared　with　the　basic　DBN　model,　SODBN-AAL　averagely　improves　learning　accuracy　by　77.13%　and　learning　efficiency　by　84.83%.　©　2015　IEEE.