Some adaptive sampling approaches have been developed to efficiently and accurately build global metamodels for the deterministic single-response problems. Most complex engineering problems, however, yield multiple responses during one simulation. This article adjusts the framework of the CV-Voronoi adaptive sampling approach for a multi-response system. In the proposed multi-response CV-Voronoi (mCV-Voronoi) sampling approach, a new strategy that combines a weighted-sum term and an extreme term is presented to properly estimate the cell errors by simultaneously considering the characteristics of multiple responses. The performance of this approach is investigated on 57 multi-response systems and two engineering design problems. The results show that mCV-Voronoi is very promising for global metamodeling of deterministic multi-response systems.