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The strategies used in solving problems can be influenced by cognitive style. This research is a qualitative descriptive study. The purpose of this study was to describe the mathematical critical thinking skills of junior high school students based on the cognitive style of Dependent Field (FD) and cognitive style Field Independent (FI) in solving SPLDV problems. The subject of this study consisted of 1 student who had the FD cognitive style and 1 student who had the FI cognitive style chosen by purposive sampling. Data collection techniques were carried out by administering the cognitive style test of the Embedded Figure Test (GEFT) Group, mathematical problem solving tests, interview guidelines, and documentation. Data were analyzed based on FRISCO critical thinking category indicators (Focus, Reason, Inference, Situation, Clarity, and Overview) in each step of problem solving, namely understanding problems, arranging plans, implementing plans, and checking again. Data analysis is done by reducing data, presenting data, and drawing conclusions. The results showed that students who had the cognitive style of FD and students who had the cognitive style FI had good critical thinking skills in each step of problem solving according to Polya.