Intelligent　computing　technologies　are　useful　and　important　for　online　data　modeling,　where　system　dynamics　may　be　nonstationary　with　some　uncertainties.　In　this　paper,　an　efficient　learning　mechanism　is　developed　for　building　self-organizing　fuzzy　neural　networks　(SOFNNs),　where　a　secondorder　algorithm　(SOA)　with　adaptive　learning　rate　is　employed,　the　network　size　and　the　parameters　can　be　determined　simultaneously　in　the　learning　process.　First,　all　parameters　of　SOFNN　are　adjusted　by　using　the　SOA　strategy　to　achieve　fast　convergence　through　a　powerful　search　scheme.　Second,　the　structure　of　SOFNN　can　be　self-organized　using　the　relative　importance　index　of　each　rule.　The　fuzzy　rules　used　in　SOFNN　with　SOA　(SOA-SOFNN)　are　generated　or　pruned　automatically　to　reduce　the　computational　complexity　and　potentially　improve　the　generalization　power.　Finally,　a　theoretical　analysis　on　the　learning　convergence　of　the　proposed　SOA-SOFNN　is　given　to　show　the　computational　efficiency.　To　demonstrate　the　merits　of　our　proposed　approach　for　data　modeling,　several　benchmark　datasets,　and　a　real　world　application　associated　with　nonlinear　systems　modeling　problems　are　examined　with　comparisons　against　other　existing　methods.　The　results　indicate　that　our　proposed　SOA-SOFNN　performs　favorably　in　terms　of　both　learning　speed　and　prediction　accuracy　for　online　data　modeling.