The purpose of the study was to produce a study of the effectiveness of CTL learning on mathematical critical thinking skills and describe students' mathematical critical thinking skills in CTL learning based on their cognitive style. The type of research used is a mixed method concurrent embedded model. The subjects of this study were eighth-grade students of SMP Ekarini Semarang. Retrieval of data in the form of cognitive style using the GEFT test and mathematical critical thinking skills through tests. The results of analysis of individual completeness data using one sample t-test sign value 0.588> 0.05, classical completeness with test proportion z count = 1.67> z table = 1.64, and simple linear regression test with the help of SPSS produces a sign value of 0,000 <0,005 with R2 = 0.684 which means that the application of effective CTL learning to mathematical critical thinking skills and cognitive style has an influence on mathematical critical thinking skills of 68.4%. The cognitive style of FDI has the best mathematical critical thinking ability by mastering the ability in aspects of conclusions, assumptions, deductions, and interpretations. The cognitive style of FI masters the ability in aspects of conclusions, deductions, interpretations, and evaluate arguments. The cognitive style of FD controls the ability to draw conclusions, assumptions, and deductions. Educa need to pay attention to the application of learning that can be received by all students despite having different styles such as cognitive the CTL models.