At present, when the time-domain discontinuous Galerkin (DGTD) method is utilizedfor solving the electromagnetic propagation problem in various media, Maxwell's equations of constitutive relation of ordinary media are usually considered. Aimed at the problems thatelectromagnet in Tellegen media with non-reciprocity constitutive relation is very complex in propagation, and few researchers care to ask about something,a matrix discrete scheme of DGTD system is derived for Tellegen medium, and the time-domain propagation characteristics of plane waves in Tellegen medium are accurately simulated based on the constitutive relation of Tellegen medium.The proposed algorithm is utilized for calculating the layered space model of air and Tellegenmedium, andanalyzing the influence of Tellegen medium on electromagnetic polarization deflection angles. Simultaneously, in view ofTellegen media with different electromagnetic parameters, the electric field deflection angles of reflected and transmitted waves are calculated, and the results calculated by the DGTD scheme are compared with the literature ［1］and the analytical solutions. And the effectiveness and feasibility of the proposed method are verified.