This study investigated the new revised Mathematics curriculums of elementary schools in Korea and Japan at the end of the 20th century. The comparison was made especially with revising direction, purposes, and contents of elementary school mathematics curriculum in both countries. I began by comparing and confirming the ratio of instruction hours of Mathematics to the total instruction hours of all the subjects at as whole. This comparison was done of the elementary and middle school mathematics. The next part of the study was to compare in detail the purposes of revised mathematics in elementary and middle schools of both countries. Particular attentions was paid to the important revised points of Japanese elementary school Mathematics. Finally, I concluded by comparing the contents of elementary school Mathematics of the two countries. New mathematic text books in both countries having been published by revised curriculum, puts the future task in comparing, in detail, the concrete contents of each textbook.