This paper reports the infrared and far-infrared spectra of TixY1-xBa2Cu3O7-δ (x = 0.2, 0.4) superconductors in the temperature range of 300K to 4.2K. Seven reflection peaks have been observed in the range of 50-360cm-1 and identified -to be associated with the vibrations of Ba, Cu, 0 ions, Y, 0 ions, Ti, 0 ions, and Cu-0 bonds respectively. For x - 0.2, two inversion structures were observed, but only one for x = 0.4. In the infrared spectra six reflection and three absorption peaks were observed, the intensities increase with the increase of the Ti content. We discussed the origin of the peaks and the inversion structures comparing with YBa2Cu3O7-δ.