A　pruning　algorithm　for　neural　network　based　on　information　entropy　is　proposed　in　this　paper.　In　the　proposed　algorithm,　a　new　e-exponential　information　entropy　of　neural　networks＇　connection　weights　is　defined　based　on　the　theory　of　Shannon＇s　information　entropy.　Although　both　information　entropies　have　approximately　the　same　description　on　uncertainty,　the　new　e-exponential　information　entropy　overcomes　the　inherent　drawbacks　of　Shannon＇s　entropy.　By　introducing　newly　defined　entropy　as　a　penalty-term　into　normal　objective　function,　the　minor　weight　connection　is　punished　and　the　major　weight　connection　is　encouraged　due　to　the　unique　property　of　entropy　function.　Therefore,　a　simple　architecture　of　neural　networks　can　be　achieved　by　deleting　the　connection　weights　whose　values　are　approximately　equal　to　zero.　The　simulation　result　using　a　typical　non-linear　function　approximation　shows　that　a　simple　architecture　of　neural　networks　can　be　achieved　and　at　the　same　time　the　performance　of　approximation　is　warranted.