In the textbook of quantum mechanics, the expression of coordinate operator in momentum representation only gives the final result, and the detailed derivation process is seldom mentioned, which will cause students to have corresponding doubts in the process of learning quantum mechanics. What is more,the expression of coordinate operator in momentum representation is deduced by using the basic assumption that free particle is plane waves and Dirac δ function, which is abstract and complex, and is not conducive to students in-depth understanding in the teaching process. In this paper, we introduce the concept of Taylor's translation on the basis of Taylor's expansion. According to the commutation relation and Taylors translation, the expression of coordinate operators in the momentum representation is derived. This method is enlightening in the teaching process and more conducive to the students understanding of this part of the content.