By utilizing the opposite thermo-optical characteristics of silicon oxynitride (SiON) and polymer materials, a hybrid integrated SiON/polymer waveguide total internal reflection (TIR) thermo-optic (TO) switch has been designed. The operation of the suggested switch is using an electrode heater, which is fabricated on a trench that is located in the center part of SiON waveguide X-junction and filled with the same polymer material as the cladding used, to adjust the refractive index of the polymer filled in the trench so as to realize TIR effect. Theoretical results show that, the suggested switch can realize an extinction ratio more than 36 dB and a crosstalk lower than -36 dB with very low driving power of 2.3 mW for TE and TM polarization by choosing the suitable polymer material which index matches that of SiON, and then by optimizing the design parameters of the single waveguide, the cross angle between the two waveguide, the width of the trench, and the structure of the electrode heater.