There are several factors that influence problem-solving abilities including cognitive styles and learning models. This research aims to analyze the profile of students' mathematical problem-solving abilities with field dependent cognitive style and to test the achievement of classical learning completeness of students in solving mathematical problems with discovery learning models. The method used in this study is the mixed methods with concurrent embedded design. Data collection techniques were carried out using the Group Embedded Figure Test (GEFT) test, Problem-solving ability (TKPM) test, interview, and documentation. Based on the analysis of obtained data that in solving the problem with Polya's steps, field dependent subjects are able to understand the problem but still uses mathematical language that resembles the problem, unable to device a plan on a particular problem that requires deeper analysis, unable to carry out the plan properly on certain questions that require more analysis  and look back the answer but cannot correct the mistake and the learning with the discovery learning model achieves average score of 77.39 of classical completeness in solving problems with which is higher then the Minimum Completeness Criteria (KKM) score of 65. Thus cognitive style is very important to be considered to determine the learning model that is suitable for students to be able to solve mathematical problems.