Mathematical Critical thinking is one of  mathematical abilities that must be obtained by students. Critical thinking is one of the high order thinking processes that can make concepts in student knowledge.  Students with critical thinking in mathematics learning mostly do rational activities such as interpreting information based on a particular theoretical framework, linking theory with practice, making claims and justifying it, utilizing data in support of argumentation, making relations or relationships between various ideas, asking questions, evaluating knowledge, predict, describe something, analyze, synthesize, and categorize. This study aims to analyze the effect of the Concept-Based Learning Model on the critical thingking mathematical abilities.The purpose of this research is to analyze the effect of Concept-Based Learning Model toward mathematics critical thinking ability. The method used in this research is quasi experiment by Randomize Control Group Post Test Only Design with cluster random sampling technique. Indicators of mathematics critical thinking skills measured in this study include providing simple explanations, building basic skills, concluding, making more explanations, and deciding an action. The results showed that the mathematics critical thinking ability of students in the experimental class for the five indicators that being analyze was higher than the ability of students in the control class. A fairly high difference in the indicator showed in give a simple explanation and concluding. and it means that the application of Concept-Based Learning Model significantly influences the  abilities  of students' mathematics critical thinking.