A　fuzzy　neural　network　(FNN)　is　an　effective　learning　system　that　combines　neural　network　and　fuzzy　logic,　which　has　achieved　great　success　in　nonlinear　system　modeling.　However,　when　the　input　is　practical　complex　data　with　external　disturbance,　the　existing　FNN　cannot　extract　effective　input　features　sufficiently,　leading　to　unsatisfactory　performances　in　learning　speed　and　accuracy.　It　also　fails　to　achieve　a　better　generalization　capability　because　of　its　fixed　structure　size　(the　number　of　rule　neurons).　In　this　article,　an　efficient　self-organizing　FNN　(SOFNN)　with　incremental　deep　pretraining　(IDPT),　called　IDPT-SOFNN,　is　developed　to　overcome　these　shortcomings.　First,　IDPT　is　designed　to　extract　effective　features　and　consider　them　as　the　input　of　the　SOFNN.　Different　from　the　existing　pretraining,　the　self-growing　structure　of　IDPT　improves　pretraining　efficiency　with　a　more　compact　structure.　Second,　the　SOFNN　can　dynamically　add　and　delete　neurons　according　to　the　current　error　and　error-reduction　rate.　In　this　case,　it　can　obtain　better　modeling　performance　with　a　more　compact　structure　as　well.　Third,　as　a　novel　hybrid　model　with　the　cascade　dual-self-organizing　algorithm,　the　IDPT-SOFNN　combines　the　advantage　of　IDPT　and　SOFNN.　Moreover,　the　convergence　and　stability　are　analyzed.　Finally,　simulation　studies　and　comparisons　demonstrate　that　the　proposed　IDPT-SOFNN　has　better　performances　than　its　peers　in　learning　speed,　accuracy,　and　generalization　capability.