Abstract: In this paper，the transmission matrix problem of a plane electromagnetic wave in one-dimensional dielectric isotropic periodic medium is extended to one -dimensional dielectric anisotropic periodic medium. The transmission matrix of a plane electromagnetic wave in such medium is obtained. The derivation of the matrix is mainly based on the Maxwell equations and continuity conditions of the electromagnetic wave at the interface of the medium. Namely，the tangential components of the electric field and magnetic field of the electromagnetic wave are continuous at the interface of the medium. The derivation of this matrix can deepen the students' understanding the course“Electromagnetic Field and Electromagnetic Wave”. This matrix is also the basis for obtaining the field distribution， the dispersion relation and surface mode properties of the electromagnetic wave in a one-dimensional dielectric anisotropic periodic medium. Therefore，this transmission matrix is of great significance for both scientific research and teaching.

Key words: plane electromagnetic wave, transmission matrix, anisotropic period