Choosing　space　Cg　as　the　phase　space,　the　existence,　uniqueness　and　stability　of　the　solution　to　neutral　stochastic　functional　differential　equations　with　infinite　delay　(short　for　INSFDEs)　are　studied　in　this　paper.　Under　non-Lipschitz　condition,　weakened　linear　growth　condition　and　contractive　condition,　the　existence-and-uniqueness　theorem　of　the　solution　to　INSFDEs　by　means　of　the　Picard　iteration,　Doob＇s　martingale　inequalities,　Gronwall＇s　inequality　and　Bihari＇s　inequality　is　obtained.　Furthermore,　the　continuous　dependence　of　the　solutions　on　the　initial　value　to　INSFDEs　are　derived.　©　2013　Wei　and　Cai;　licensee　Springer.