In this paper, design of rectangular iris waveguide filter for the microwave broadcasting transponder using WR137 is applied to the modified ${TE^x}_{mn}$ mode theory in order to exactly analyze the characteristic of the waveguide discontinuity. We designed and fabricated the rectangular iris waveguide filter with the bandwidth 47 MHz for the microwave broadcasting transponder applied the conjugate gradient method to the modified ${TE^x}_{mn}$ mode theory. The results show a good characteristics that the $S_{11}$ and $S_{21}$ are -23 ㏈, -0.56 ㏈ and the maximum VSWR is below 1.02 in the passband.