This　paper　proposes　a　novel　method　to　improve　accuracy　and　speed　for　traveling　salesman　problem　(TSP).　A　novel　hysteretic　noisy　frequency　conversion　sinusoidal　chaotic　neural　network　(HNFCSCNN)　with　improved　energy　function　is　proposed　for　TSP　to　improve　the　solution　quality　and　reduce　the　computational　complexity.　HNFCSCNN　combines　chaotic　searching,　stochastic　wandering　with　hysteretic　dynamics　for　better　global　searching　ability.　A　specific　activation　function　with　two　hysteretic　loops　in　different　directions　is　adopted　to　relieve　the　adverse　impact　caused　by　higher　noise　for　frequency　conversion　sinusoidal　chaotic　neural　network　(FCSCNN).　A　new　modified　energy　function　for　TSP　which　has　lower　computational　complexity　than　the　previous　energy　function　is　established.　The　simulation　results　show　that　the　proposed　HNFCSCNN　can　increase　the　optimization　accuracy　and　speed　of　FCSCNN　at　higher　noises,　and　that　the　proposed　energy　function　can　decrease　the　runtime　of　optimal　computation.　It　has　better　optimization　performance　than　the　other　several　algorithms.