Approaching　to　the　biological　neural　network,　small-world　neural　networks　have　been　demonstrated　to　improve　the　generalization　performance　of　artificial　neural　networks.　However,　the　architecture　of　small-world　neural　networks　is　typically　large　and　predefined.　This　may　cause　the　problems　of　overfitting　and　time　consuming,　and　cannot　obtain　an　optimal　network　structure　automatically　for　a　given　problem.　To　solve　the　above　problems,　this　paper　proposes　a　pruning　feedforward　small-world　neural　network　(PFSWNN),　and　applies　it　to　nonlinear　system　modeling.　Firstly,　a　feedforward　small-world　neural　network　(FSWNN)　is　constructed　according　to　the　rewiring　rule　of　Watts-Strogatz.　Secondly,　the　importance　of　each　hidden　neuron　is　evaluated　based　on　its　Katz　centrality.　If　the　Katz　centrality　of　a　hidden　neuron　is　below　the　predefined　threshold,　this　neuron　is　considered　to　be　an　unimportant　node　and　then　merged　with　its　most　correlated　neuron　in　the　same　hidden　layer.　The　connection　weights　are　trained　using　the　gradient-based　algorithm,　and　the　convergence　of　the　proposed　PFSWNN　is　theoretically　analyzed　in　this　paper.　Finally,　the　PFSWNN　model　is　tested　on　some　problems　for　nonlinear　system　modeling,　including　the　approximation　for　a　rapidly　changing　function,　CATS　missing　time-series　prediction,　four　benchmark　problems　of　UCI　public　datasets　and　a　practical　problem　for　wastewater　treatment　process.　Experimental　results　demonstrate　that　PFSWNN　exhibits　superior　generalization　performance　by　small-world　property　as　well　as　the　pruning　algorithm,　and　the　training　time　of　PFSWNN　is　shortened　owning　to　a　compact　structure.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.