Education aims to improve the quality of human life which is technically through lectures. A good lecture produces a positive influence on students' ability. The interaction between lecturers and students in the class is an important role in achieving the goals. Linear Algebra is an important subject in the Mathematic. Many students think that Linear Algebra are difficult. Linear Algebra at the Faculty of Computer Science, Dharma AUB University of Surakarta have not been able to improve students' understanding of Linear Algebra concepts. Because of class that are centered on lecturers. Based on the description above, the author applies the TAPPS (Thinking Aloud Pair Problem Solving) cooperative learning model to increase concept understanding of Linear Algebra. Formulation of the problem in this research: "Is there an increase concept understanding of Linear Algebra after using the TAPPS learning model?". This research is a qualitative descriptive group with the type of Classroom Action Research. The data used are field notes and documentation. Based on the research results, it can be concluded that there is an increase in understanding of the concept of Linear Algebra through the TAPPS (Thinking Aloud Pair Problem Solving) model.