In the present research, the high-order DG-ADER method is used to solve governing equations of two-phase drift flux model. The drift flux model is suitable for studying two-phase flows where the phases are strongly coupled. This model is composed of three differential equations including two continuity equations for two phases and a mixture momentum equation. The mixture model uses also an algebraic relation to link the velocity of the phases. The high-order DG-ADER numerical method, which is a new scheme to get high order accuracy of results, is used to solve the governing equations. The DG-ADER is a nonlinear method in which the reconstruction process is performed using WENO method and the time evolution part is achieved by discontinues Galerkine approach. The results are compared with those reported by other researchers. Three problems including two two-phase shock tubes and a pure rarefaction test problem are solved using this method. The results show that DG-ADER method can solve the two-phase flow problems with a very good accuracy even on a coarse grid. The drawback of this method is presenting numerical fluctuations with limited domain at the position of shock waves.