By employing Lagrangian function and Lsubdifferential approach，the global optimal sufficient conditions for a class of cubic programming problem involving bivalent and inequality constrains is researched.Firstly，the abstract subdifferential for Lagrangian function of the class of cubic programming problems is calculated explicitly.Then some global optimal sufficient conditions for cubic programming problem with bivalent and inequality constrains are obtained.Finally，some examples are given to illustrate the optimality conditions.