This paper proposes a cumulative function approximation based on Voronoi diagram, a technique of computational geometry, and an adaptive global optimization by using the approximation. The proposed approximation method represents a global function by blending local quadratic polynomials approximating the subspaces around respective sample points based on the geometric structure that is manipulated by Voronoi diagram. It can be used as an adaptive medium between system analysis and optimization computation under its superposability. That is, an adaptive global optimization scheme is configured by the iteration of establishing approximation with initial samples, executing optimization over approximation, adaptively arranging new samples and refining approximation. It can gradually update the fidelity of approximation in a process of optimization and find the global optimum with less times of system analysis. The validity and effectiveness of the proposed scheme is ascertained through numerical examples.