Conceptual understanding skills is very important for student as fundamental learning to solve problem and to develop knowledge from various experiences or previous understanding. The successful learning on mathematic need of mathematical conversant from each learner. Mathematic practitioner highly hope could create mathematically proficient individuals. This study aims to describe the success and challenges of proficient students in implementing conceptual understanding to solve mathematical problems. It used the descriptive qualitative method. The data were collected through tests and semi-structured interviews. Purposive sampling was use to choose the research subject, that were three students who got the highest score on mathematic last examination from acceleration class of SMAN 11 Tangerang. Then, the data were analyzed through data reduction, data presentation, and drawing conclusions. Validity of data using technical triangulation. As a result, the students with proficient category have both achievement and obstacle in order to implement conceptual understanding on mathematical problem. As for obstacle problem shown where they could not restate the early stage of problem solving. While, their excess looked from how they use trial and error strategy in problem solving contexts. This strategy came from any idea and logically thought from any previous understanding which each student has in this category.
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