By using Lagrangian function and subdifferential approach, this paper presents some sufficient global optimality conditions for a cubic programming problem with binary constraints, and in some special cases, the results obtained in this paper are equivalent to some corresponding results in reference ［9］. An example is given to demonstrate that the optimality conditions can effectively be applied to identifying global minimizers of the certain noncovex cubic minimization problem. The results improve and generalize the corresponding ones in the reference ［9］.