TE01 bends play an important role in the High Power Microwave(HPM) system. TE01 bends should bear higher power and wider band width as the HPM develops towards higher power and wider band. TE01 bends designed by traditional method have the disadvantages of narrow band and limited power capacity. The bottleneck of TE01 bend design is the existence of TM11, which is the degenerated mode of TE01. In this paper，a Chebyshev design method based on the elliptical waveguide is proposed, and in the elliptical waveguide, the TE01 and TM11 are no longer the degenerated modes. The coupled mode theory is adopted to finish the design procedure. A Ka band TE01 bend is theoretically designed, and the semi-major axis and semi-minor axis are 7 mm and 5.25 mm, respectively. Computer simulation results show that the frequency ranges from 32 GHz to 45.1 GHz(mode preserve efficiency keeps above 95%), and the effectiveness is verified.