<em>This research aims at improving mathematical reasoning skills through the implementation of Realistic Mathematics Education approach. This is a two-cycles Classroom Action Research (CAR). Each cycle consists of three meetings. There are four stages in every meeting that are planning, acting, observing, and reflecting. The subject of this research is 30 students of the fifth grade of SD Negeri Tunggulsari 1 Surakarta, academic year 2019/2020. Observation, interview, tests, and documentation are used as the data collection technique. Triangulation is used to check the validity of this research. The data are analyzed using Miles- Huberman interactive analysis model. The result of the first cycle shows that the students' classical mastery is 43%, while the second cycle is 80%. Those results indicate that the mathematical reasoning skill of the fifth grade students of SD Negeri Tunggulsari 1 Surakarta academic year 2019/2020 can be improved by the implementation of Realistic Mathematics Education approach.</em>