A　modified　difference　Hopfield　neural　network　is　proposed　to　overcome　the　multiple　local　minimum　problem　of　normal　difference　Hopfield　neural　network.　On　conditions　that　the　modified　Hopfield　neural　network　works　in　a　parallel　mode　and　its　interconnection　weight　matrix　is　negative,　it　has　only　one　stable　state,　and　the　stable　state　can　make　its　energy　function　reach　to　its　only　minimum.　On　the　basis　of　the　relation　between　the　stability　of　the　modified　difference　Hopfield　network　and　its　energy　function＇s　convergence,　the　modified　Hopfield　network　is　applied　to　solve　LQ　dynamic　optimization　control　problems　for　time-varying　systems.　It　can　be　constructed　by　building　the　equivalence　between　the　energy　function　of　the　modified　Hopfield　network　and　the　performance　Index　of　controlled　system.　As　a　result,　solving　LQ　dynamic　optimization　control　problem　is　equivalent　to　operating　associated　modified　difference　Hopfield　network　from　any　initial　state　to　the　stable　state　that　represents　the　desired　optimal　control　vector.　The　simulation　results　agree　well　with　theoretical　analysis.　©　2005　IEEE.