This research is aimed at finding out: (1) the influence of discovery learning model with RME approach on Mathematics learning achievement; (2) the influence of interpersonal intelligence on Mathematics learning achievement; and (3) the interaction between discovery learning model with RME approach and interpersonal intelligence on Mathematics learning achievement. The research was conducted at one of the state Elementary Schools in Banjarsari sub-district, Surakarta. The method used in this research was quasi-experimental method with 2x3 factorial design. Hypothesis test was done by two-way variance ANOVA test with different cells. It can be concluded that the discovery learning model with RME approach gives better influence on the Mathematics learning achievement than the direct learning model. Students having high interpersonal intelligence category get better Mathematics learning achievement than those having medium and low category. The students having medium interpersonal intelligence get better Mathematics achievement than those having low category. There is no interaction between learning model and interpersonal intelligence on Mathematics learning achievement.