In　this　paper,　we　introduce　the　conception　of　(h,　ψ)-generalized　second-order　directional　derivatives　of　real　function　in　Banach　space　and　discuss　some　of　their　properties　and　their　relationships.　In　order　to　define　above　conceptions,　we　generalize　the　Ben-Tal＇s　generalized　algebraic　operations　in　Euclidean　space　to　Banach　space.　©　2011　Springer-Verlag　Berlin　Heidelberg.