The purpose of the research was to increase students' critical thinking skills in mathematics by applying the Realistic Mathematics Education (RME) model. The type of research method is Classroom Action Research (PTK) which is carried out in 2 cycles. Each cycle consists of planning, implementation, observation, and reflection. The subjects of classroom action research were fourth grade students of SD Negeri 34 Lubuklinggau totaling 19 students consisting of 10 female students and 9 male students. Data collection techniques using observation and tests. The result from this reasearch showed that by applying the Realistic Mathematics Education (RME) model can increase the ability of critical thinking mathematics students in fourth grade SD Negeri 34 Lubuklinggau. It can be seen from the increasing students' critical thinking skills in mathematics from the pre-cycle condition of 54%, cycle I of applying the Realistic Mathematics Education (RME) model for critical thinking skills of 69%, based on deficiencies in cycle I then followed up in cycle II, the results of critical thinking skills at this stage increased to 80.5%. It is concluded that the application of the Realistic Mathematics Education (RME) model can increase students' mathematical critical thinking skills in fourth grade SD Negeri 34 Lubuklinggau.