A broadband rectangular waveguide TE 10-TE 20 mode converter with high mode purity and conversion efficiency is designed, fabricated and measured in this Letter. Based on the broadband characteristic of ridged twist waveguide and its characteristic of polarisation direction torsion of electromagnetic wave, this mode converter achieves broadband and high-efficiency TE 10-TE 20 mode conversion. Simulation results reveal that the return loss of the proposed mode converter is >20 dB and insertion loss is <0.04 dB in whole Ka-band. Two prototype TE 20 mode converters were fabricated. Back-to-back millimeter-wave measurements by vector network analyser were performed to verify the design. The measured performances show return loss of the proposed mode converter is >20 dB and insertion loss is <0.1 dB in whole Ka-band, the corresponding mode conversion efficiency is >97.7%.