Mathematical self-efficacy and the snowball-throwing learning model play a role in student learning success. Mathematical self-efficacy is a student's perception of mathematical abilities. The study aimed to analyze students' critical thinking skills based on mathematical self-efficacy through the application of the snowball-throwing learning model to material composition functions. The research method uses a qualitative with the type of case study research. The number of respondents consisted of three students representing high, medium, and low mathematical self-efficacy categories. The research instrument used tests of critical thinking skills, questionnaires, and interviews. The data analysis technique uses three stages, namely data reduction, data presentation, and conclusion the data. The results of the study were obtained as follows: 1) Students who have high mathematical self-efficacy have high critical thinking skills with all indicators of critical thinking skills fulfilled, 2) Students who have moderate mathematical self-efficacy have critical thinking skills with only one indicator fulfilled, and 3) Students who have low mathematical self-efficacy do not have all indicators of critical thinking skills. Learning the composition function using the snowball-throwing learning model is appropriate when used for students who have a high level of mathematical self-efficacy to train students' critical thinking skills.