Single-mode operation in a rectangular waveguide is very important, since the existence of multimodes may arouse distortions of carried signals due to the modal dispersion. High-order mode means multiple periods of field in the transverse cross section, with distinct electromagnetic properties from the dominant mode. Although numerous methods are proposed to achieve mode selection within the waveguide, they only permit specific high-order modes to survive in a frequency range. However, it still remains a great challenge to control the bandwidth freely for single-mode operation. Here, we propose an approach for high-order mode generation, in which the desired mode operates in the band gap of other modes, and the working bandwidth can be engineered independently by reducing the symmetry of the loaded periodic metallic ridges in the waveguide. Two examples are demonstrated, where only
TE
20
and
TE
30
modes are supported. The proposed method can also be applied to generate other high-order TE modes in the future.