The optimization problems of binary functions widely exist in many practical engineering problems,their global optimization methods have always been one of the hot research issues. A high effective method of global optimization to nonnegative binary functions was put forward basing on the maximum modulus theorem of the analytic function of complex function,this method can simplify the optimization problem of the object function on a two-dimension bounded area as an one-dimension global optimization problem,the theory basis for the optimization method was given,and three numerical examples were given to show the effectiveness of the method. On one hand,the conclusions obtained in this paper can be directly used to solve the optimization problem in which the analytic function theory could be used,on the other hand,it can be used to obtain the global optimization solutions of the two-dimension mathematical optimization problems in which the method could be used in a high precision and high effective manner.