By　integrating　the　small-world　(SW)　property　into　the　design　of　feedforward　neural　networks,　the　network　performance　would　be　improved　by　well-documented　evidence.　To　achieve　the　structural　self-adaptation　of　the　feedforward　small-world　neural　networks　(FSWNNs),　a　self-organizing　FSWNN,　namely　SOFSWNN,　is　proposed　based　on　a　hub-based　self-organizing　algorithm　in　this　paper.　Firstly,　an　FSWNN　is　constructed　according　to　Watts-Strogatz＇s　rule.　Derived　from　the　graph　theory,　the　hub　centrality　is　calculated　for　each　hidden　neuron　and　then　used　as　a　measurement　for　its　importance.　The　self-organizing　algorithm　is　designed　by　splitting　important　neurons　and　merging　unimportant　neurons　with　their　correlated　neurons,　and　the　convergence　of　this　algorithm　can　be　guaranteed　theoretically.　Extensive　experiments　are　conducted　to　validate　the　effectiveness　and　superiority　of　SOFSWNN　for　both　classification　and　regression　problems.　SOFSWNN　achieves　an　improved　generalization　performance　by　SW　property　and　the　self-organizing　structure.　Besides,　the　hub-based　self-organizing　algorithm　would　determine　a　compact　and　stable　network　structure　adaptively　even　from　different　initial　structure.　©　2017　IEEE.