An algorithm for global optimization of a class of nonconvex MINLP problems is developed and presented in this paper. By partitioning the variables, dual representation of the primal of subproblems and outer-approximation strategy are used to develop a representative relaxed iterative problem. Then the original MINLP problem is replaced by a series of subproblems and relaxed iterative problems. By exploiting the particular form of the nonconvex MINLP problem, the feasible region of this problem is explicitly included in the representative problem, thus the inconvenience encountered with the GBD method can be avoided. The proposed method is illustrated and interpreted geometrically with an example problem.