Today, people need to prepare key competencies demanded for life to be worthy of individual and to be successful for not only individual life but development of society. We can look for these competencies in the process of analysing of present and future society. On the basis of this cognition we desire to suggest certain key competencies in korea mathematics curriculum and to investigate how to realize them in this paper. First, we investigated key competencies demanded generally from several articles to deal with key competencies. Secondly, we inspected backgrounds and processes of implementing mathematics curriculum in Korea and Japan and checked the reason for laying key competencies on the center of curriculum. Thirdly, we arranged key competencies suggested in mathematics curriculum of two countries and compared how to realize them. Finally, on the ground of third contents we proposed current affairs to Korea mathematics curriculum.