In　this　article,　the　generalized　Roper-Suffridge　extension　operator　in　Banach　spaces　for　locally　biholomorphic　mappings　is　introduced.　It　is　proved　that　this　operator　preserves　the　starlikeness　on　some　domains　in　Banach　spaces　but　does　not　preserves　convexity　for　some　cases.　Moreover,　the　growth　theorem,　covering　theorem,　and　the　radius　of　starlikeness　are　discussed.　Some　results　of　Roper　and　Suffridge,　Gong　and　Liu,　Graham　et　al　in　Cn　are　extended　to　Hilbert　spaces　or　Banach　spaces.　©　2008　Wuhan　Institute　of　Physics　and　Mathematics.