Feedforward　neural　networks　(FNNs)　with　a　single　hidden　layer　have　been　widely　applied　in　data　modeling　due　to　its＇　universal　approximation　capability　to　nonlinear　maps.　However,　such　a　theoretical　result　does　not　provide　with　any　guideline　to　determine　the　architecture　of　the　model　in　practice.　Thus,　researches　on　self-organization　of　FNNs　are　useful　and　critical　for　effective　data　modeling.　This　paper　proposes　a　hybrid　constructing　and　pruning　strategy　(HCPS)　for　problem　solving,　where　the　mutual　information　(MI)　and　sensitivity　analysis　(SA)　are　employed　to　measure　the　amount　of　internal　information　of　neurons　at　the　hidden　layer　and　the　contribution　rate　of　each　hidden　neuron,　respectively.　HCPS　merges　hidden　neurons　when　their　MI　value　becomes　too　high,　deletes　hidden　neurons　when　their　contribution　rates　are　sufficiently　small,　and　splits　hidden　neurons　when　their　contribution　rates　are　very　big.　For　each　instant　pattern　feed　into　the　model　as　a　training　sample,　the　weights　of　the　neural　network　will　be　updated　to　ensure　the　model＇s　output　unchanged　during　structural　adjustment.　HCPS　aims　to　get　a　condensed　model　through　eliminating　redundant　neurons　and　without　degrading　the　instant　modeling　performance,　which　is　associated　with　the　model＇s　generalization　property.　The　proposed　algorithm　is　evaluated　by　some　benchmark　data　sets,　including　classification　problems,　a　non-linear　system　identification　problem,　a　time-series　prediction　problem,　and　a　real　world　application　for　pM(2.5)　predictions.　Simulation　results　with　comparisons　demonstrate　that　our　proposed　method　performs　favorably　and　has　improved　the　existing　work　in　terms　of　modeling　performance.　(C)　2017　Elsevier　B.V.　All　rights　reserved.